A XIONIC S TRINGS AND I NFINITE F IELD D ISTANCE A XIONIC S TRINGS IN - - PowerPoint PPT Presentation

SWAMPLAND CONJECTURES

FOR STRINGS AND MEMBRANES

Summer Series on String Phenomenology ~ September 1, 2020

based on arXiv: 2006.15154 with Fernando Marchesano, Luca Martucci, Irene Valenzuela

Stefano Lanza

HARVARD UNIVERSITY

Extended objects with low codimension strongly backreact on the geometry; in 4D

LOW CODIMENSION OBJECTS AND BACKREACTIONS

Backreaction negligible as r → ∞ Particle Strong backreaction as the distance from the source increases, with the metric breaking down at a finite distance from the object String Membrane

STRONG BACKREACTIONS AND EFTS

How can we understand the backreaction of the objects at EFT level? Does the inclusion of strings or membranes break the EFT? RG flow of the EFT couplings We will show this correspondence in N=1 Supergravity EFTs. Backreaction of the extended objects

• nto the spacetime metric and the fields of the EFT

[Goldberger, Wise 2001; Polchinski et al. 2014]

EXTENDED OBJECTS AND SWAMPLAND CONJECTURES

No Global Symmetries

Completeness hypothesis

Trivial bordism group

Weak Gravity Conjecture

Distance Conjecture

Instability of non- supersymmetric AdS vacua

No de Sitter Conjecture

AdS distance Conjecture

Repulsive Force Conjecture Transplanckian Censorship Conjecture

EXTENDED OBJECTS AND SWAMPLAND CONJECTURES

No Global Symmetries

Completeness hypothesis

Trivial bordism group

Weak Gravity Conjecture

Distance Conjecture

Instability of non- supersymmetric AdS vacua

No de Sitter Conjecture

AdS distance Conjecture

Repulsive Force Conjecture Transplanckian Censorship Conjecture

EXTENDED OBJECTS AND SWAMPLAND CONJECTURES

No Global Symmetries

Completeness hypothesis

Trivial bordism group

Weak Gravity Conjecture

Distance Conjecture

Instability of non- supersymmetric AdS vacua

No de Sitter Conjecture

AdS distance Conjecture

Repulsive Force Conjecture Transplanckian Censorship Conjecture

Axionic Strings

EXTENDED OBJECTS AND SWAMPLAND CONJECTURES

No Global Symmetries

Completeness hypothesis

Trivial bordism group

Weak Gravity Conjecture

Distance Conjecture

Instability of non- supersymmetric AdS vacua

No de Sitter Conjecture

AdS distance Conjecture

Repulsive Force Conjecture Transplanckian Censorship Conjecture

Membranes

AXIONIC STRINGS

AND INFINITE FIELD DISTANCE

AXIONIC STRINGS IN N=1 SUPERGRAVITY

We will consider fundamental axionic strings: they are included directly within the EFT as fundamental objects, with strict codimension two; electrically coupled to gauge two-forms via: magnetically coupled to the dual axions: In order to embed fundamental strings in Supergravity, we need a proper formulation which supersymmetrically includes gauge 2-forms. In order to consider strings semiclassically within an EFT with cutoff Λ, their tension needs to satisfy

The bosonic components of an N=1 supersymmetric action of a set of chiral multiplets is Assume that the Kähler potential is invariant under axionic shifts:

Φi

AXIONIC STRINGS IN N=1 SUPERGRAVITY

saxions axions The dual action expressed in terms of a set of linear multiplets is and Ν=1 supersymmetry fixes the scalar metric and gauge kinetic function to be equal:

[SL, Marchesano, Martucci, Sorokin, 2019]

Dualize the chiral multiplets to linear multiplets . At the bosonic level:

Φi Li

axions (gauge 0-forms)

saxions

dual saxions gauge 2-forms

We can now couple a fundamental string: with

AXIONIC STRINGS IN N=1 SUPERGRAVITY

The string tension is fixed by supersymmetry: The physical string charge is defined by The string tension obeys the tautological identity

Over its worldsheet, the string preserves at most 1/2 of the bulk supersymmetry, the other half being nonlinearly realized.

with

N = 1 bulk susy N = 1 worldvolume susy

Solving the equations of motions gives the backreacted solution: for the saxion and axion for the warp factor

s a

THE STRING BACKREACTION

Consider a single string located at radial coordinate and whose worldvolume is described by the coordinates . Metric ansatz with , coordinates transverse to the string and .

r = 0 t, x z ¯ z r = |z|

Consider a single saxion , entering the Kähler potential as

s

The solution breaks down at a finite distance r

THE STRING BACKREACTION AS RG FLOW

The flow of the tension is which breaks down at a distance In the limit :

r → 0

Define the energy scale Consider the string tension as EFT coupling

We regard the profile of the tension as RG-flow of the tension and the EFT breaks at the strong coupling scale On the other hand, the limit corresponds to weak coupling.

r → 0

RFC FOR AXIONIC STRINGS

Two identical strings interact with the following forces

No gravitational forces Scalar forces

Supersymmetric strings trivially satisfy the no-force condition The Repulsive Force Conjecture requires the existence of self-repulsive elementary axionic strings satisfying: which has to hold scale-wise along the RG-flow.

Electric forces

[Palti, 2017; Heidenreich, Reece, Rudelius, 2019]

WGC FOR AXIONIC STRINGS

Weak Gravity Conjecture for strings: a super-extremal string satisfying with being the extremality factor.

∃ γ

How to determine the extremality factor? For single scalar field, with Kähler potential the extremality factor is specified by the no-scale factor Recall that a BPS-string satisfies the no-force condition For multiple scalar fields, asymptotically in field space, we can use the sl(2) orbit theorem to approximate using which it can be shown with

[Arkani-Hamed et al. 2006; Heidenreich, Reece, Rudelius, 2015; Reece, 2018; Craig et al. 2018, …]

The limit , with corresponds to infinite field distance

• r:

r → 0

AXIONIC STRINGS AND INFINITE FIELD DISTANCES

• 1. As

, the EFT cutoff exponentially decreases: dmax → ∞

• 2. Close to the string, infinite oscillatory modes become massless, with fall off of the masses

The string extremality factor fixes the rate at which the masses become massless [see also Gendler, Valenzuela, ’20]

⇒

string WGC d → ∞

si → ∞

,

Distant Axionic String Conjecture (DASC): All infinite distance limits of a 4d EFT can be realised as an RG flow endpoint of a fundamental axionic string.

THE DISTANT AXIONIC STRING CONJECTURE

For finite cutoff Λ, the moduli space is

• nly partially explorable.

Infinite field distances are ideally explorable when Λ , corresponding to the endpoint of the string RG flow.

→ 0

Changing Λ =RG flow

Distant Axionic String Conjecture (DASC): All infinite distance limits of a 4d EFT can be realised as an RG flow endpoint of a fundamental axionic string.

THE DISTANT AXIONIC STRING CONJECTURE

Infinite field distances are ideally explorable when Λ , corresponding to the endpoint of the string RG flow.

→ 0

Infinite tower of states become massless KK modes, D0 branes, … → 0 with r ≥ 1 [SL, Marchesano, Martucci, Valenzuela, to appear]

MEMBRANES

AND SCALAR POTENTIAL

MEMBRANES IN N=1 SUPERGRAVITY

We will consider fundamental membranes:

• bjects with strict codimension one;

electrically coupled to a set of gauge three-forms: In order for the membranes to be treated semiclassically within an EFT with cutoff Λ, their tension needs to satisfy Embedding membranes in Supergravity requires a formulation that supersymmetrically includes gauge three-forms.

First step: including gauge three-forms in N=1 supergravity Introduce the modified chiral multiplets and construct the N=1 supersymmetric action where is the inverse of

Tab

MEMBRANES IN N=1 SUPERGRAVITY

: holomorphic periods with

Integrating out the gauge three-forms via

• ne gets

with the scalar potential

and Gauge three-forms dual of fluxes

Second step: including supersymmetric membranes Fundamental membranes can be included as with

MEMBRANES IN N=1 SUPERGRAVITY

The potential ‘jumps’ as the membrane is crossed The membrane modifies the 3-form eoms.

Second step: including supersymmetric membranes Fundamental membranes can be included as with

MEMBRANES IN N=1 SUPERGRAVITY

The membrane tension is fixed by supersymmetry The physical charge is defined as

BPS membranes tautologically satisfy

GENERATING MEMBRANES

with

Compare with the scalar potential

They coincide for generating membranes. They interpolate between a fluxless region and one with a nontrivial flux: which implies ‘Generating membrane’

THE MEMBRANE BACKREACTION

Asymptotically in field space, we can use the sl(2) orbit theorem to approximate and assume we can single out a monomial with the maximal growth so that [Grimm, Li, Palti, Valenzuela, … ’18-‘20] with discrete data that specify the asymptotic limit with For a supersymmetric domain wall with metric ansatz the warp factor and the membrane tension backreactions are ‘Generating membrane’

The backreaction onto the tension is which breaks at the distance from the membrane. It is regular in the limit

y → 0

THE MEMBRANE BACKREACTION AS RG-FLOW

Define the energy scale Consider the membrane tension as EFT coupling

We regard the profile of the tension as RG-flow of the tension and the EFT breaks at the strong coupling scale The membrane tension increases as .

Λ → Λstrong

Two identical membranes interact with the following constant forces

THE RFC FOR MEMBRANES

Scalar forces

The Repulsive Force Conjecture requires the existence of self-repulsive elementary membranes, satisfying: which has to hold scale-wise along the RG-flow. Supersymmetric membranes trivially satisfy the no-force condition

Gravitational forces

[Vilenkin 1981]

Electric forces

[see also Garriga, Megevand 2003; Herráez 2020] [Palti, 2017; Heidenreich, Reece, Rudelius, 2019]

THE WGC FOR MEMBRANES

Weak Gravity Conjecture for membranes: a super-extremal membrane satisfying with being the extremality factor.

∃ γ

A BPS-membrane satisfies which is not in a “WGC-like form”. with Asymptotically in field space, for a saxionic membrane satisfying the physical charge becomes proportional to the membrane tension with the extremality factor How to determine the extremality factor?

[Arkani-Hamed et al. 2006; Heidenreich, Reece, Rudelius, 2015; Font, Ibanez, Herraez 2018 …]

EXTREMAL MEMBRANES AND THE DE SITTER CONJECTURE

with Consider an extremal membrane, obeying and assume that this membrane fully generates a potential with the physical charge: Asymptotically in field space, for elementary membranes The potential so generated obeys the de Sitter conjecture [Vafa et al. 2018] The minimal value of is

c

with

CONCLUSIONS

The strong backreaction of low-codimension objects can be understood as RG flow of the EFT couplings; Physical quantities, such as tensions and charges, are scale dependent, changing along the flow;

CONCLUSIONS AND FUTURE OUTLOOK

RFC and WGC for low-codimension objects; WGC strings Distance Conjecture WGC saturating membranes de Sitter Conjecture

⇒ ⇒

These conclusions are expected to hold also for different spacetime dimensions, provided that the codimension of the objects is kept fixed; Possible relation RG-flow and vacua decay? Extension to non-supersymmetric cases?

Thank you!