Supertubes Supersymmetric Black Black Rings Rings Supertubes - - PowerPoint PPT Presentation

Supersymmetric Supersymmetric Black Black Rings Rings

S1 S2

David David Mateos Mateos

and and Supertubes Supertubes

• Emparan & DM, to appear
• Microscopic Entropy of the Black Ring [hep-th/0411187]
• M. Cyrier, M. Guica, DM & A. Strominger
• A Supersymmetric Black Ring [hep-th/0407065]
• H. Elvang, R. Emparan, DM & H. Reall
• Supersymmetric Black Rings and 3-charge Supertubes [hep-th/0408120]
• H. Elvang, R. Emparan, DM & H. Reall
• Supertubes [hep-th/0103030]

DM & P. Townsend

• Supergravity Supertubes [hep-th/0106012]
• R. Emparan, DM & P. Townsend
• Tachyons, Supertubes and Brane/anti-Brane Systems [hep-th/0112054]

DM, S. Ng & P. Townsend

• Supercurves [hep-th/0204062]

DM, S. Ng & P. Townsend

Black Ring = Asymptotically Flat,

Stationary Black Hole Solution in 5D with Horizon Topology S1 × × × × S2

S1 S2

× × × × flat directions = Black Supertube

Why are Black Rings interesting? D=4 M, J, Q D=5: Black Ring M, Q, J, …

Emparan & Reall

Why are Supersymmetric BRs interesting?

• Establish non-uniqueness in susy sector
• Establish stability of Black Rings
• Implications for microscopic entropy calculation

→ → → → Not only counting BPS states with same charges is not enough, it is also not right!

• Provide ideal arena to study these issues because:

susy + know microscopic constituents + stability mechanism

• Expose how little we know about gravitational physics in D>4

Plan

2-charge

Basic Mechanism: Supertubes

3-charge

Supergravity Description WV Description Microscopic Entropy AdS/CFT Description Conclusions

2-charge Supertubes: Worldvolume Description

DM & Townsend

Supersymmetric Brane Expansion in Flat Space by Angular Momentum F1 D0

E B P Tubular D2/F1/D0 Bound State

1/4-SUSY preserved QF1 and QD0 dissolved as fluxes J generated as integrated Poynting E = QF1 + QD0 Arbitrary Cross-section C C C C in

• 8:

(and charge densities) TS-Dualizing = `Helical’ String with Left-moving wave on it No net D2-brane charge but dipole qD2 ∼ ∼ ∼ ∼ nD2

J

¼-SUSY

C C C C

P J

2-charge Supertubes: Supergravity Description

No net D2 charge, but D2 dipole (and higher) moments: ψ ψ ψ ψ Easily understood ~ D2/anti-D2 pair: x

Emparan, DM & Townsend

3-charge Supertubes and Supersymmetric Black Rings: Supergravity Description

Elvang, Emparan, DM & Reall Bena & Warner Gauntlett & Gutowski

T34 Lift First, lift 2-charge supertube to M-theory: Ring solution with regular horizon → → → → 3 charges Best microscopic description → → → → M-theory 6 4 = 2 (r, ψ) × 2 (ρ, φ ) ψ ψ ψ ψ φ r R ρ ρ ρ ρ × time = 5D black ring metric With 3 charges, each pair expands:

ψ ψ ψ ψ φ r R ρ ρ ρ ρ

New feature: Jφ

φ φ φ ≠

≠ ≠ ≠ 0

7 parameters: R, Qi , qi 5 conserved charges: Qi , Jψ

ψ ψ ψ and Jφ φ φ φ

Infinite violation of uniqueness by 2 continuous parameters Choosing Qi, qi and Jψ

ψ ψ ψ as independent parameters:

Black String Limit

Send R → → → → ∞ ∞ ∞ ∞ keeping Qi / R and qi fixed Important: Jψ

ψ ψ ψ →

→ → → Pψ

ψ ψ ψ ≠

≠ ≠ ≠ 0

but Jφ

φ φ φ →

→ → → 0 !

Black string solution of Bena ψ S2

12

M2 3456ψ M5 E B

E × × × × B = 0

12

M2 3456ψ M5 E B

E × × × × B ∝ ∝ ∝ ∝ Q1 q1 + Q2 q2 + Q3 q3 – q1 q2 q3 Suggests Jφ

φ φ φ is Poynting-generated by SUGRA fields

Jφ

φ φ φ ∼

∼ ∼ ∼ ∫ ∫ ∫ ∫ T0φ

φ φ φ ∼

∼ ∼ ∼ ∫ ∫ ∫ ∫ E × × × × B

Components of D=11 SUGRA F4

Worldvolume 3-charge Supertubes

Elvang, Emparan, D.M. & Reall

First step: F1/D4/D0 bound state with D2/D6/NS5 dipoles

Bena & Kraus Gibbons & Papadopoulos Gauntlett, Lambert & West

Problematic in open string description

Circumvented in M-theory: Single M5-brane =

Holomorphic 2-surface in

• 6

7 Turning on H induces M2 charge and allows arbitrary C C

In summary: Captures 3 dipoles, Jφ

φ φ φ = 0

Microscopic Entropy Counting

Single M5-brane =

Holomorphic 2-surface in

• 6

S1

• 1,3

4D black hole

Maldacena, Strominger & Witten; Vafa

(0,4) CFT with cleft= 6q1q2q3 and left-moving momentum p

M-theory on

• 6

× × × × S1 × × × ×

• 1,3

p’ = p + M2-induced shift + zero-point shift

Microscopic Entropy Counting

Cyrier, Guica, DM & Strominger

Single M5-brane =

Holomorphic 2-surface in

• 6

S1 in

• 1,4

5D black ring

(0,4) CFT with cleft= 6q1q2q3 and left-moving momentum p = Jψ

ψ ψ ψ

Counts states with Jφ

φ φ φ=0 !!!

M-theory on

• 6

× × × ×

• 1,4

3-charge Supertubes D1/D5/P System

Elvang, Emparan, DM & Reall Bena & Kraus

Same CFT describes Black Hole and Black Ring

Decoupling limit: α α α α’ → → → → 0 , r /α α α α’ fixed, etc.

RG >

Supersymmetric Supersymmetric Black Black Rings Rings

S1 S2

Supertubes Supertubes

=

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