David Mateos- Supersymmetric Black Rings and Supertubes

8/3/2019 David Mateos- Supersymmetric Black Rings and Supertubes

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SupersymmetricSupersymmetric BlackBlack RingsRings

S 1

S 2

DavidDavid MateosMateos

andand

SupertubesSupertubes



• 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 5Dwith Horizon Topology S 1 ×××× S 2

S 1

S 2

×××× flat directions = Black Supertube



Why are Black Rings interesting?

D=4M, J, Q

D=5: Black RingM, 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-chargeBasic Mechanism: Supertubes

3-charge

Supergravity DescriptionWV DescriptionMicroscopic EntropyAdS/CFT DescriptionConclusions



2-charge Supertubes: Worldvolume Description DM & Townsend

Supersymmetric Brane Expansion in Flat Space by Angular Momentum

F1

D0

E

BP

Tubular D2/ F1 /D0Bound State

1/4-SUSY preserved

QF1 and QD0 dissolved as fluxesJ generated as integrated PoyntingE = Q F1 + Q D0

Arbitrary Cross-section C CC C in EEEE 8:(and charge densities)

TS-Dualizing = `Helical’ String withLeft-moving wave on it

No net D2-brane chargebut dipole q D2 ∼∼∼∼ n D2

J

¼-SUSY

C CC C

P

J



2-charge Supertubes: Supergravity Description

No net D2 charge, but D2 dipole (and higher) moments:

ψ ψψ ψ

Easily understood ~ D2/anti-D2 pair:

x

Emparan, DM & Townsend



3-charge Supertubes and Supersymmetric Black Rings:Supergravity Description

Elvang, Emparan, DM & ReallBena & WarnerGauntlett & Gutowski

T34 Lift

First, lift 2-charge supertube to M-theory:

Ring solution with regular horizon →→→→ 3 charges

Best microscopic description →→→→ M-theory

T 6 E 4 = E 2 (r, ψ) × E 2 (ρ , φ )

ψ ψψ ψ

φ

r

R

ρρρρ

× time = 5D black ring metric

With 3 charges, each pair expands:



ψ ψψ ψ

φ

r

R

ρρρρNew feature: J φφφφ ≠≠≠≠ 0

7 parameters: R, Q i , q i

5 conserved charges: Q i , J ψ ψψ ψ and J φφφφ

Infinite violation of uniqueness by 2 continuous parameters

Choosing Q i, q i and J ψ ψψ ψ as independent parameters:



Black String Limit

Send R →→→→ ∞∞∞∞ keeping Q i / R and q i fixed

Important: J ψ ψψ ψ →→→→ P ψ ψψ ψ ≠≠≠≠ 0 but J φφφφ →→→→ 0 !

Black string solution of Bena

ψ

S 2

12

M23456 ψ

M5

E B

E ×××× B = 0

12

M23456 ψ

M5

E B

E ×××× B ∝∝∝∝ Q1 q 1 + Q 2 q 2 + Q 3 q 3 – q 1 q 2 q 3

Suggests J φφφφ is Poynting-generated by SUGRA fields J φφφφ ∼∼∼∼ ∫ ∫∫ ∫ T0φφφφ ∼∼∼∼ ∫ ∫∫ ∫ E ×××× B

Components ofD=11 SUGRA F 4



Worldvolume 3-charge Supertubes

Elvang, Emparan, D.M. & Reall

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

Gibbons & PapadopoulosGauntlett, Lambert & West

Problematic in openstring description

Circumvented in M-theory:

Single M5-brane =

Holomorphic 2-surface in TTTT 6

7

Turning on H induces M2 charge and allows arbitrary C

C

In summary: Captures 3 dipoles, J φφφφ = 0



Microscopic Entropy Counting

Single M5-brane =

Holomorphic 2-surface in TTTT 6 S 1 RRRR 1,3

4D black hole

Maldacena, Strominger & Witten; Vafa

(0,4) CFT with c left = 6q 1q 2q 3 and left-moving momentum p

M-theory on TTTT 6 ×××× S 1 ×××× RRRR 1,3

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



Microscopic Entropy Counting Cyrier, Guica, DM & Strominger

Single M5-brane =

Holomorphic 2-surface inTTTT 6

S1

inRRRR 1,4

5D black ring

(0,4) CFT with c left = 6q 1q 2q 3 and left-moving momentum p = J ψ ψψ ψ

Counts states with J φφφφ=0 !!!

M-theory on TTTT 6 ×××× RRRR 1,4



3-charge Supertubes D1/D5/P System Elvang, Emparan, DM & ReallBena & Kraus

Same CFT describes Black Hole and Black Ring

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

RG

>



SupersymmetricSupersymmetric BlackBlack RingsRings

S 1

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SupertubesSupertubes=MESSAGEMESSAGE

David Mateos- Supersymmetric Black Rings and Supertubes

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