The Calabi-Yau Landscape: Beyond the Lampposts Mehmet Demirtas - - PowerPoint PPT Presentation

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The Calabi-Yau Landscape: Beyond the Lampposts Mehmet Demirtas - - PowerPoint PPT Presentation

Feb 04, 2023 42 likes •952 views

The Calabi-Yau Landscape: Beyond the Lampposts Mehmet Demirtas Cornell University String Pheno Series, 2020 Based on works with (various subsets of): Manki Kim, Cody Long, Liam McAllister, Jakob Moritz, Mike Stillman, Andres Rios Tascon What

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The Calabi-Yau Landscape: Beyond the Lampposts

Mehmet Demirtas

Cornell University String Pheno Series, 2020

Based on works with (various subsets of): Manki Kim, Cody Long, Liam McAllister, Jakob Moritz, Mike Stillman, Andres Rios Tascon

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SLIDE 2

What is possible in quantum gravity?

  • de-Sitter solutions?
  • Super-Planckian field ranges?
  • Quintessence?
  • Global symmetries?
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What is possible in quantum gravity?

  • de-Sitter solutions?
  • Super-Planckian field ranges?
  • Quintessence?
  • Global symmetries?

What is generic in quantum gravity?

  • Ultralight axions?
  • Light dark sectors?
  • Exponential hierarchies?
  • Light moduli?
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SLIDE 4

What is possible in quantum gravity?

  • de-Sitter solutions?
  • Super-Planckian field ranges?
  • Quintessence?
  • Global symmetries?

What is generic in quantum gravity?

  • Ultralight axions?
  • Light dark sectors?

A primary method: Study solutions of string theory.

  • Exponential hierarchies?
  • Light moduli?
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SLIDE 5

What is possible in quantum gravity?

  • de-Sitter solutions?
  • Super-Planckian field ranges?
  • Quintessence?
  • Global symmetries?

What is generic in quantum gravity?

  • Ultralight axions?
  • Light dark sectors?

A primary method: Study solutions of string theory. Can answer for: Weakly coupled compactifications of superstring theories.

  • Exponential hierarchies?
  • Light moduli?
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SLIDE 6

To get started: Compactifications on simple Calabi-Yau (CY) manifolds with small Hodge numbers.

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To get started: Compactifications on simple Calabi-Yau (CY) manifolds with small Hodge numbers.

Picture taken from Aliexpress.com. (You can buy this lamppost!)

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To get started: Compactifications on simple Calabi-Yau (CY) manifolds with small Hodge numbers.

Picture taken from Aliexpress.com. (You can buy this lamppost!)

However: this is an exponentially small fraction of the String Landscape.

  • Number of (known) topologically

inequivalent CY manifolds increases exponentially with .

  • Number of flux vacua in type IIB (F-

Theory) compactifications increases exponentially with ( ).

[MD, McAllister, Rios Tascon, hep-th/2008.01730] [Denef, Douglas, hep-th/0404116] [Denef, Douglas, hep-th/0411183] [Taylor, Wang, hep-th/1511.03209]

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We can now construct CY threefolds with largest known Hodge numbers and compute relevant topological data.

Kreuzer-Skarke

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Outline

I. CY3’s from Triangulations II. Holomorphic Cycles

Application: Ultralight Axions

  • III. 3-cycles

Application: Towards KKLT

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A Quick Review

  • This talk: CY threefolds.
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A Quick Review

  • This talk: CY threefolds.
  • Largest known set of CY threefolds: hypersurfaces in toric varieties.

[Batyrev, alg-geom/9310003] [Kreuzer, Skarke, hep-th/0002240]

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A Quick Review

  • This talk: CY threefolds.
  • Largest known set of CY threefolds: hypersurfaces in toric varieties.

The construction:

1. Take a 4D reflexive lattice polytope

Reflexive: the only interior point of the polytope (and its dual) is the origin. [Batyrev, alg-geom/9310003] [Batyrev, alg-geom/9310003] [Kreuzer, Skarke, hep-th/0002240]

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A Quick Review

  • This talk: CY threefolds.
  • Largest known set of CY threefolds: hypersurfaces in toric varieties.

The construction:

1. Take a 4D reflexive lattice polytope

Reflexive: the only interior point of the polytope (and its dual) is the origin.

2. Obtain a (fine, regular, star) triangulation

[Batyrev, alg-geom/9310003] [Batyrev, alg-geom/9310003] [Kreuzer, Skarke, hep-th/0002240]

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A Quick Review

  • This talk: CY threefolds.
  • Largest known set of CY threefolds: hypersurfaces in toric varieties.

The construction:

1. Take a 4D reflexive lattice polytope

Reflexive: the only interior point of the polytope (and its dual) is the origin.

2. Obtain a (fine, regular, star) triangulation This triangulation defines a fan, which describes a toric variety V that has a CY hypersurface X.

[Batyrev, alg-geom/9310003] [Batyrev, alg-geom/9310003] [Kreuzer, Skarke, hep-th/0002240]

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The number of reflexive lattice polytopes:

  • In 2D: 16
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The number of reflexive lattice polytopes:

  • In 2D: 16
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The number of reflexive lattice polytopes:

  • In 2D: 16
  • In 3D: 4,319
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The number of reflexive lattice polytopes:

  • In 2D: 16
  • In 3D: 4,319
  • In 4D: 473,800,776

[Kreuzer, Skarke, hep-th/0002240]

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Reflexive polytopes in 4 dimensions

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Reflexive polytopes in 4 dimensions

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Reflexive polytopes in 4 dimensions

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The number of reflexive lattice polytopes:

  • In 2D: 16
  • In 3D: 4,319
  • In 4D: 473,800,776

Number of triangulations

  • Number of lattice points on the polytope
  • [Kreuzer, Skarke, hep-th/0002240]
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SLIDE 24

How many CY3 hypersurfaces are there?

The number of reflexive lattice polytopes:

  • In 2D: 16
  • In 3D: 4,319
  • In 4D: 473,800,776

Number of triangulations

  • Number of lattice points on the polytope
  • [Kreuzer, Skarke, hep-th/0002240]
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How many CY3 hypersurfaces are there?

  • Not known.
  • We recently proved an upper bound of .

The number of reflexive lattice polytopes:

  • In 2D: 16
  • In 3D: 4,319
  • In 4D: 473,800,776

Number of triangulations

  • Number of lattice points on the polytope
  • [MD, McAllister, Rios Tascon, hep-th/2008.01730]

[Kreuzer, Skarke, hep-th/0002240]

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Notation:

  • : 4D Ambient Variety, X: Calabi-Yau threefold hypersurface

Holomorphic Cycles

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Notation:

  • : 4D Ambient Variety, X: Calabi-Yau threefold hypersurface
  • Mori cone:

is the cone of effective curves.

Holomorphic Cycles

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Notation:

  • : 4D Ambient Variety, X: Calabi-Yau threefold hypersurface
  • Mori cone:

is the cone of effective curves.

  • Kähler cone:

is the set of cohomology classes of Kähler forms.

Holomorphic Cycles

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Notation:

  • : 4D Ambient Variety, X: Calabi-Yau threefold hypersurface
  • Mori cone:

is the cone of effective curves.

  • Kähler cone:

is the set of cohomology classes of Kähler forms.

  • are dual cones:

Holomorphic Cycles

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Notation:

  • : 4D Ambient Variety, X: Calabi-Yau threefold hypersurface
  • Mori cone:

is the cone of effective curves.

  • Kähler cone:

is the set of cohomology classes of Kähler forms.

  • are dual cones:
  • No general algorithm for computing in hypersurfaces.
  • Can compute on a case-by-case basis.
  • Can compute .

Holomorphic Cycles

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Holomorphic Cycles

  • Volumes of 2-cycles , 4-cycles , and itself

are determined by the Kähler form and the intersection numbers: where span .

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Holomorphic Cycles

  • Volumes of 2-cycles , 4-cycles , and itself

are determined by the Kähler form and the intersection numbers: where span .

  • Stretched Kähler cone:
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Kähler cone generator

Mori cone generator

Kähler cone

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Kähler cone generator

Mori cone generator

Stretched Kähler cone

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Holomorphic Cycles

  • Volumes of 2-cycles , 4-cycles , and itself

are determined by the Kähler form and the intersection numbers: where span .

  • Stretched Kähler cone:

estimate for the convergence of the worldsheet instanton expansion and the control of the expansion.

[Candelas, De La Ossa, Green, Parkes, ‘90]

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Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
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Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
  • Many, systematic studies.

[Braun, Walliser, hep-th/1106.4529] [Blumenhagen, Gao, Rahn, Shukla, hep-th/1205.2485] [Gao, Shukla, hep-th/1307.1139] [Altman, Gray, He, Jejjala, Nelson, hep-th/1411.1418] [Cicoli, Muia, Shukla, hep-th/1611.04612] [Braun, Lukas, Sun, hep-th/1704.07812] [Altman, He, Jejjala, Nelson, hep-th/1706.09070] [Long, McAllister, Stout, hep-th/1603.01259] [Cicoli, Ciupke, Mayrhofer, Shukla, hep-th/1801.05434] [Carifio, Cunningham, Halverson, Krioukov, Long, Nelson, hep-th/1711.06685] … many more!

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Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
  • Many, systematic studies.
  • Few, limited studies.

[Braun, Walliser, hep-th/1106.4529] [Blumenhagen, Gao, Rahn, Shukla, hep-th/1205.2485] [Gao, Shukla, hep-th/1307.1139] [Altman, Gray, He, Jejjala, Nelson, hep-th/1411.1418] [Cicoli, Muia, Shukla, hep-th/1611.04612] [Braun, Lukas, Sun, hep-th/1704.07812] [Altman, He, Jejjala, Nelson, hep-th/1706.09070] [Long, McAllister, Stout, hep-th/1603.01259] [Cicoli, Ciupke, Mayrhofer, Shukla, hep-th/1801.05434] [Carifio, Cunningham, Halverson, Krioukov, Long, Nelson, hep-th/1711.06685] … many more! [Long, McAllister, McGuirk, hep-th/1407.0709] [Long, McAllister, Stout, hep-th/1603.01259] [Halverson, Long, hep-th/2001.00555]

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Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
  • Many, systematic studies.
  • Few, limited studies.
  • Only recently.

[Braun, Walliser, hep-th/1106.4529] [Blumenhagen, Gao, Rahn, Shukla, hep-th/1205.2485] [Gao, Shukla, hep-th/1307.1139] [Altman, Gray, He, Jejjala, Nelson, hep-th/1411.1418] [Cicoli, Muia, Shukla, hep-th/1611.04612] [Braun, Lukas, Sun, hep-th/1704.07812] [Altman, He, Jejjala, Nelson, hep-th/1706.09070] [Long, McAllister, Stout, hep-th/1603.01259] [Cicoli, Ciupke, Mayrhofer, Shukla, hep-th/1801.05434] [Carifio, Cunningham, Halverson, Krioukov, Long, Nelson, hep-th/1711.06685] … many more! [Long, McAllister, McGuirk, hep-th/1407.0709] [Long, McAllister, Stout, hep-th/1603.01259] [Halverson, Long, hep-th/2001.00555] [MD, Long, McAllister, Stillman, hep-th/1808.01282] [Halverson, Long, Nelson, Salinas, hep-th/1909.05257] [MD, McAllister, Rios Tascon, hep-th/2008.01730]

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SLIDE 40

Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
  • Many, systematic studies.
  • Few, limited studies.
  • Problem: Computations get expensive rapidly with .
  • There are 19,849,166 intersection numbers at !
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SLIDE 41

Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
  • Many, systematic studies.
  • Few, limited studies.
  • Problem: Computations get expensive rapidly with .
  • There are 19,849,166 intersection numbers at !
  • Solution: Start from scratch, rewrite everything.
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SLIDE 42

Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
  • Many, systematic studies.
  • Few, limited studies.
  • Problem: Computations get expensive rapidly with .
  • There are 19,849,166 intersection numbers at !
  • Solution: Start from scratch, rewrite everything.

Obtain one triangulation

[MD, McAllister, Rios Tascon, hep-th/2008.01730]

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Recent Advances

  • Recap: Need to triangulate a reflexive polytope and compute intersection

numbers.

  • Can be done via open source math software, like Sage.
  • Many, systematic studies.
  • Few, limited studies.
  • Problem: Computations get expensive rapidly with .
  • There are 19,849,166 intersection numbers at !
  • Solution: Start from scratch, rewrite everything.

Compute intersection numbers Obtain one triangulation

[MD, McAllister, Rios Tascon, hep-th/2008.01730] [MD, McAllister, Rios Tascon, hep-th/2008.01730]

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Introducing: CYTools

A software package for constructing CY hypersurfaces in toric varieties.

[MD, McAllister, Rios Tascon, work in progress]

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Introducing: CYTools

A software package for constructing CY hypersurfaces in toric varieties. Can construct a CY and compute intersection numbers in a few lines of code:

vertices=[[1,0,0,0],[0,1,0,0],[0,0,0,1],[21,28,36,42],[-63,-56,-48,-42]] poly=LatticePolytope(vertices) triangulation=poly.triangulate() triangulation.intersection_numbers()

[MD, McAllister, Rios Tascon, work in progress]

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Introducing: CYTools

A software package for constructing CY hypersurfaces in toric varieties. Can construct a CY and compute intersection numbers in a few lines of code:

vertices=[[1,0,0,0],[0,1,0,0],[0,0,0,1],[21,28,36,42],[-63,-56,-48,-42]] poly=LatticePolytope(vertices) triangulation=poly.triangulate() triangulation.intersection_numbers()

  • Lattice points on the polytope
  • The dual polytope
  • Faces, dual faces of the polytope
  • GLSM charge matrix
  • Stanley-Reisner ideal
  • Second Chern class
  • Mori cone of the ambient variety
  • Stretched Kähler cone
  • Volumes of cycles
  • … many more!

Can compute:

[MD, McAllister, Rios Tascon, work in progress]

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Introducing: CYTools

A software package for constructing CY hypersurfaces in toric varieties. Can construct a CY and compute intersection numbers in a few lines of code:

vertices=[[1,0,0,0],[0,1,0,0],[0,0,0,1],[21,28,36,42],[-63,-56,-48,-42]] poly=LatticePolytope(vertices) triangulation=poly.triangulate() triangulation.intersection_numbers()

  • Lattice points on the polytope
  • The dual polytope
  • Faces, dual faces of the polytope
  • GLSM charge matrix
  • Stanley-Reisner ideal
  • Second Chern class
  • Mori cone of the ambient variety
  • Stretched Kähler cone
  • Volumes of cycles
  • … many more!

Can compute: Many orders of magnitude faster than Sage.

[MD, McAllister, Rios Tascon, work in progress]

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SLIDE 48

Introducing: CYTools

A software package for constructing CY hypersurfaces in toric varieties. Can construct a CY and compute intersection numbers in a few lines of code:

vertices=[[1,0,0,0],[0,1,0,0],[0,0,0,1],[21,28,36,42],[-63,-56,-48,-42]] poly=LatticePolytope(vertices) triangulation=poly.triangulate() triangulation.intersection_numbers()

  • Lattice points on the polytope
  • The dual polytope
  • Faces, dual faces of the polytope
  • GLSM charge matrix
  • Stanley-Reisner ideal
  • Second Chern class
  • Mori cone of the ambient variety
  • Stretched Kähler cone
  • Volumes of cycles
  • … many more!

Aside: Some of these quantities can be predicted using Machine Learning.

  • Achieved using a deep neural net. High precision even at .
  • per prediction. A further speed-up of a factor of .

Can compute: Many orders of magnitude faster than Sage.

[MD, McAllister, Rios Tascon, hep-th/2008.01730] [MD, McAllister, Rios Tascon, work in progress]

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What is generic in the Calabi-Yau hypersurface landscape?

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Construct Ensembles of Geometries Detect Patterns Study Consequences Method:

What is generic in the Calabi-Yau hypersurface landscape?

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Pattern: At large , Kähler cones are narrow.

  • Stretched Kähler cone is far away from the origin.

Construct Ensembles of Geometries Detect Patterns Study Consequences Method:

What is generic in the Calabi-Yau hypersurface landscape?

[MD, Long, McAllister, Stillman, hep-th/1808.01282]

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Kähler cone generator

Mori cone generator

Stretched Kähler cone

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Stretched Kähler cone

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SLIDE 54

Pattern: At large , Kähler cones are narrow.

  • Stretched Kähler cone is far away from the origin.
  • Volumes of effective 2-cycles, 4-cycles and the CY itself are large.

Construct Ensembles of Geometries Detect Patterns Study Consequences Method:

What is generic in the Calabi-Yau hypersurface landscape?

[MD, Long, McAllister, Stillman, hep-th/1808.01282]

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Consequences:

Consider type IIB compactified on an O3/O7 orientifold of X.

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Consequences:

Consider type IIB compactified on an O3/O7 orientifold of X. axions: get a potential from non-perturbative objects (ED3s, D7 branes) wrapping 4- cycles,

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SLIDE 57

Consequences:

Consider type IIB compactified on an O3/O7 orientifold of X. axions: get a potential from non-perturbative objects (ED3s, D7 branes) wrapping 4- cycles, Large 4-cycles → Suppressed potential → Ultralight axions!

[MD, Long, McAllister, Stillman, hep-th/1808.01282]

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Consequences:

Consider type IIB compactified on an O3/O7 orientifold of X. axions: get a potential from non-perturbative objects (ED3s, D7 branes) wrapping 4- cycles, Large 4-cycles → Suppressed potential → Ultralight axions! →Black hole superradiance (See Viraf’s talk!)

[MD, Long, McAllister, Stillman, hep-th/1808.01282] [MD, Long, Marsh, McAllister, Mehta, Stott, work in progress]

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SLIDE 59

Consequences:

Consider type IIB compactified on an O3/O7 orientifold of X. axions: get a potential from non-perturbative objects (ED3s, D7 branes) wrapping 4- cycles, Large 4-cycles → Suppressed potential → Ultralight axions! →Black hole superradiance (See Viraf’s talk!) Further Consequences:

  • Hierarchies in 4-cycle volumes → Realizing KKLT is hard.

[MD, Long, McAllister, Stillman, hep-th/1808.01282] [MD, Long, Marsh, McAllister, Mehta, Stott, work in progress]

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SLIDE 60

Consequences:

Consider type IIB compactified on an O3/O7 orientifold of X. axions: get a potential from non-perturbative objects (ED3s, D7 branes) wrapping 4- cycles, Large 4-cycles → Suppressed potential → Ultralight axions! →Black hole superradiance (See Viraf’s talk!) Further Consequences:

  • Hierarchies in 4-cycle volumes → Realizing KKLT is hard.
  • Large 4-cycles → Rich 7-brane dark sector.

[MD, Long, McAllister, Stillman, hep-th/1808.01282] [MD, Long, Marsh, McAllister, Mehta, Stott, work in progress] [Cvetic, Halverson, Lin, Long, hep-th/2004.00630]

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SLIDE 61

Consequences:

Consider type IIB compactified on an O3/O7 orientifold of X. axions: get a potential from non-perturbative objects (ED3s, D7 branes) wrapping 4- cycles, Large 4-cycles → Suppressed potential → Ultralight axions! →Black hole superradiance (See Viraf’s talk!) Further Consequences:

  • Hierarchies in 4-cycle volumes → Realizing KKLT is hard.
  • Large 4-cycles → Rich 7-brane dark sector.
  • Implications for fitting warped throats in compactifications

[MD, Long, McAllister, Stillman, hep-th/1808.01282] [MD, Long, Marsh, McAllister, Mehta, Stott, work in progress] [Cvetic, Halverson, Lin, Long, hep-th/2004.00630] [Carta, Moritz, Westphal, hep-th/1902.01412]

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SLIDE 62

Periods of 3-cycles

To study flux compactifications, we need to compute the periods of 3-cycles.

  • Pick a basis of , such that
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SLIDE 63

Periods of 3-cycles

To study flux compactifications, we need to compute the periods of 3-cycles.

  • Pick a basis of , such that
  • Periods:

where is the holomorphic 3-form and are the complex structure moduli.

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SLIDE 64

Periods of 3-cycles

To study flux compactifications, we need to compute the periods of 3-cycles.

  • Pick a basis of , such that
  • Periods:

where is the holomorphic 3-form and are the complex structure moduli.

  • Can be written in terms of a prepotential :
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SLIDE 65

Periods of 3-cycles

  • Around a large complex structure point,
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SLIDE 66

Periods of 3-cycles

  • Around a large complex structure point,
  • To compute the periods we need to identify an integral basis of 3-cycles.
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SLIDE 67

Periods of 3-cycles

  • Around a large complex structure point,

Mirror Symmetry:

Integral 3-cycles in X Integral 2n-cycles in X

  • To compute the periods we need to identify an integral basis of 3-cycles.
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SLIDE 68

Periods of 3-cycles

  • Around a large complex structure point,
  • To compute the periods we need to identify an integral basis of 3-cycles.
  • Coefficients of depend on the geometric data of holomorphic cycles in .

Mirror Symmetry:

Integral 3-cycles in X Integral 2n-cycles in X

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SLIDE 69

Periods of 3-cycles

  • Around a large complex structure point,
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SLIDE 70

Periods of 3-cycles

  • Around a large complex structure point,
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SLIDE 71
  • Around a large complex structure point,

Periods of 3-cycles

where are the genus zero Gopakumar-Vafa invariants.

[Gopakumar, Vafa, hep-th/9809187] [Gopakumar, Vafa, hep-th/9812127]

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SLIDE 72

Periods of 3-cycles

  • Around a large complex structure point,

where are the genus zero Gopakumar-Vafa invariants.

  • Existing methods allow for computing when .
  • Also, hardly any results unless is smooth and simplicial.

[Gopakumar, Vafa, hep-th/9809187] [Gopakumar, Vafa, hep-th/9812127] [Greene, Plesser, ‘90] [Candelas, De La Ossa, Green, Parkes, ‘90] [Batyrev, alg-geom/9310003] [Hosono, Klemm, Theisen, Yau, hep-th/9308122] [Hosono, Klemm, Theisen, Yau, hep-th/9406055] … and more

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SLIDE 73

Periods of 3-cycles

  • Around a large complex structure point,

where are the genus zero Gopakumar-Vafa invariants.

  • Existing methods allow for computing when .
  • Also, hardly any results unless is smooth and simplicial.
  • Now: can compute systematically for .
  • No requirements on ,
  • Up to for some curves!

[Gopakumar, Vafa, hep-th/9809187] [Gopakumar, Vafa, hep-th/9812127] [MD, Kim, McAllister, Moritz, Rios Tascon, work in progress]

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Is a de-Sitter solution possible in quantum gravity?

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SLIDE 75

Is a de-Sitter solution possible in quantum gravity?

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario. [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]
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SLIDE 76

Is a de-Sitter solution possible in quantum gravity?

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • 2. Strongly warped throat
  • 3. Non-perturbative effects to stabilize Kähler moduli
  • 4. Anti-D3 brane to uplift

[Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

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SLIDE 77

Is a de-Sitter solution possible in quantum gravity?

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • 2. Strongly warped throat
  • 3. Non-perturbative effects to stabilize Kähler moduli
  • 4. Anti-D3 brane to uplift

[Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

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SLIDE 78

Is a de-Sitter solution possible in quantum gravity?

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • 2. Strongly warped throat
  • 3. Non-perturbative effects to stabilize Kähler moduli
  • 4. Anti-D3 brane to uplift

[Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-79
SLIDE 79

Is a de-Sitter solution possible in quantum gravity?

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • 2. Strongly warped throat
  • 3. Non-perturbative effects to stabilize Kähler moduli
  • 4. Anti-D3 brane to uplift

[Ashok, Douglas, hep-th/0307049], [Denef, Douglas, hep-th/0404116], [Denef, Douglas, hep-th/0411183] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-80
SLIDE 80

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124]

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:

Is a de-Sitter solution possible in quantum gravity?

[Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-81
SLIDE 81

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:
  • An algorithm: Depends on the holomorphic data of .

Is a de-Sitter solution possible in quantum gravity?

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124] [MD, Kim, McAllister, Moritz, hep-th/1912.10047] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-82
SLIDE 82

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:
  • An algorithm: Depends on the holomorphic data of .
  • An example with .

Is a de-Sitter solution possible in quantum gravity?

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124] [MD, Kim, McAllister, Moritz, hep-th/1912.10047] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-83
SLIDE 83

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:
  • An algorithm: Depends on the holomorphic data of .
  • An example with .

Is a de-Sitter solution possible in quantum gravity?

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124] [MD, Kim, McAllister, Moritz, hep-th/1912.10047] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-84
SLIDE 84

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:
  • An algorithm: Depends on the holomorphic data of .
  • An example with .

2. Strongly warped throat

Is a de-Sitter solution possible in quantum gravity?

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124] [MD, Kim, McAllister, Moritz, hep-th/1912.10047] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-85
SLIDE 85

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:
  • An algorithm: Depends on the holomorphic data of .
  • An example with .

2. Strongly warped throat

  • Can analytically continue to near a conifold point and use the same algorithm.
  • Bonus: a method for obtaining orientifolds at .

Is a de-Sitter solution possible in quantum gravity?

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124] [MD, Kim, McAllister, Moritz, hep-th/1912.10047] [MD, Kim, McAllister, Moritz, hep-th/2009.03312] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-86
SLIDE 86

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:
  • An algorithm: Depends on the holomorphic data of .
  • An example with .

2. Strongly warped throat

  • Can analytically continue to near a conifold point and use the same algorithm.
  • Bonus: a method for obtaining orientifolds at .
  • Independently:

Is a de-Sitter solution possible in quantum gravity?

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124] [MD, Kim, McAllister, Moritz, hep-th/1912.10047] [MD, Kim, McAllister, Moritz, hep-th/2009.03312] [Blumenhagen, Alvarez-Garcia, Brinkmann, Schlechter, hep-th/2009.03325] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-87
SLIDE 87

Ultimate Goal: An explicit construction of a dS vacuum.

  • A leading candidate: the KKLT scenario.

Requires:

  • 1. Exponentially small flux superpotential
  • Until recently:
  • An algorithm: Depends on the holomorphic data of .
  • An example with .

2. Strongly warped throat

  • Can analytically continue to near a conifold point and use the same algorithm.
  • Bonus: a method for obtaining orientifolds at .
  • Independently:

Is a de-Sitter solution possible in quantum gravity?

[Denef, Douglas, Florea, hep-th/0404257] [Denef, Douglas, Florea, Grassi, Kachru, hep-th/0503124] [MD, Kim, McAllister, Moritz, hep-th/1912.10047] [MD, Kim, McAllister, Moritz, hep-th/2009.03312] [Blumenhagen, Alvarez-Garcia, Brinkmann, Schlechter, hep-th/2009.03325] [Kachru, Kallosh, Linde, Trivedi, hep-th/0301240]

slide-88
SLIDE 88

Summary

  • We can efficiently construct CY threefolds with large Hodge

numbers.

  • Can compute volumes and periods of cycles, intersection numbers, etc.
  • CYTools: A Software Package for Analyzing CY Hypersurfaces
slide-89
SLIDE 89

Summary

  • We can efficiently construct CY threefolds with large Hodge

numbers.

  • Can compute volumes and periods of cycles, intersection numbers, etc.
  • CYTools: A Software Package for Analyzing CY Hypersurfaces
  • Enables many applications
  • 1. Narrow Kähler cones → Ultralight axions
  • 2. Towards KKLT: Small flux superpotential, strongly warped throats
slide-90
SLIDE 90

Summary

  • We can efficiently construct CY threefolds with large Hodge

numbers.

  • Can compute volumes and periods of cycles, intersection numbers, etc.
  • CYTools: A Software Package for Analyzing CY Hypersurfaces
  • Enables many applications
  • 1. Narrow Kähler cones → Ultralight axions
  • 2. Towards KKLT: Small flux superpotential, strongly warped throats
  • Whenever we access a new regime of the Landscape, we encounter

surprises!

slide-91
SLIDE 91

Summary

  • We can efficiently construct CY threefolds with large Hodge

numbers.

  • Can compute volumes and periods of cycles, intersection numbers, etc.
  • CYTools: A Software Package for Analyzing CY Hypersurfaces
  • Enables many applications
  • 1. Narrow Kähler cones → Ultralight axions
  • 2. Towards KKLT: Small flux superpotential, strongly warped throats
  • Whenever we access a new regime of the Landscape, we encounter

surprises!

THANK YOU!