Microscopic Entropy of Black RingsMicroscopic Entropy of Black RingsTrobada de Nadal 2004 a ECMTrobada de Nadal 2004 a ECM

S1

S2

David MateosDavid Mateos

•Microscopic Entropy of the Black Ring [hep-th/0411187] M. Cyrier, M. Guica, D.M. & A. Strominger

•A Supersymmetric Black Ring [hep-th/0407065] H. Elvang, R. Emparan, D.M. & H. Reall

•Supersymmetric Black Rings and 3-charge Supertubes [hep-th/0408120] H. Elvang, R. Emparan, D.M. & H. Reall

•Supertubes [hep-th/0103030] D.M. & P. Townsend

•Supergravity Supertubes [hep-th/0106012] R. Emparan, D.M. & P. Townsend

•Tachyons, Supertubes and Brane/anti-Brane Systems [hep-th/0112054] D.M., S. Ng & P. Townsend

•Supercurves [hep-th/0204062] D.M., 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 Supersymmetric BRs interesting?

• Establish stability and non-uniqueness in susy sector

(In 4D ! S2, in 5D ! Emparan & Reall)

• Implication 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

2-charge Supertubes: Worldvolume Description D.M. & 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 fluxesJ generated as integrated PoyntingE = QF1 + QD0

Arbitrary Cross-section C in E8:(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

P

J

2-charge Supertubes: Supergravity Description Emparan, D.M. & Townsend

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

Easily understood ~ D2/anti-D2 pair:

x

3-charge Supertubes and Supersymmetric Black Rings:Supergravity Description

Elvang, Emparan, D.M. & 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

T6 E4 = E2 (r, £ E2 (, )

r

R

£ time = 5D black ring metric

With 3 charges, each pair expands:

r

R

New feature: J 0

7 parameters: R, Qi , qi

5 conserved charges: Qi , J and J

Infinite violation of uniqueness

Choosing Qi, qi and J as independent parameters:

Black String Limit

Send R ! 1 keeping Qi / R and qi fixed

Important: J ! P 0 but J ! 0 !

Black string solution of Bena

S2

12

M23456

M5

E B

E £ B = 0

12

M23456

M5

E B

E £ B / Q1 q1 + Q2 q2 + Q3 q3 – q1 q2 q3

Suggests J is Poynting-generated by SUGRA fields J » s T0 » s 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 & PapadopoulosGauntlett, Lambert & West

Problematic in openstring description

Circumvented in M-theory:

Single M5-brane =

Holomorphic 2-surface in T6

7

Turning on H induces M2 charge and allows arbitrary C

C

In summary: Captures 3 dipoles, J = 0

Microscopic Entropy Counting

Single M5-brane =

Holomorphic 2-surface in T6 S1 R1,3

4D black hole

Maldacena, Strominger & Witten; Vafa

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

p’ = p + M2-induced shift

M-theory on T6 £ S1 £ R1,3

Microscopic Entropy Counting Cyrier, Guica, D.M. & Strominger

Single M5-brane =

Holomorphic 2-surface in T6 S1 in R1,4

5D black ring

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

Counts states with J=0 !!!

M-theory on T6 £ R1,4

One conclusion:

Microscopic constituents of Susy Black Rings

= Supertubes

One open question:

Microscopic versus macroscopic descriptions?

or

J ?

3-charge Supertubes D1/D5/P System Elvang, Emparan, D.M & ReallBena & Kraus

Same CFT describes Black Hole and Black Ring

Decoupling limit: ’ ! 0 , r /’ fixed, etc.

RG

>