Microscopic Entropy of Black Rings Trobada de Nadal 2004 a ECM S1S1 S2S2 David Mateos

Microscopic Entropy of the Black Ring [hep-th/ ] M. Cyrier, M. Guica, D.M. & A. Strominger A Supersymmetric Black Ring [hep-th/ ] H. Elvang, R. Emparan, D.M. & H. Reall Supersymmetric Black Rings and 3-charge Supertubes [hep-th/ ] H. Elvang, R. Emparan, D.M. & H. Reall Supertubes [hep-th/ ] D.M. & P. Townsend Supergravity Supertubes [hep-th/ ] R. Emparan, D.M. & P. Townsend Tachyons, Supertubes and Brane/anti-Brane Systems [hep-th/ ] D.M., S. Ng & P. Townsend Supercurves [hep-th/ ] D.M., S. Ng & P. Townsend

Black Ring = Asymptotically Flat, Stationary Black Hole Solution in 5D with Horizon Topology S 1 £ S 2 S1S1 S2S2 £ flat directions = Black Supertube

Why are Supersymmetric BRs interesting? Establish stability and non-uniqueness in susy sector (In 4D ! S 2, 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 Q F1 and Q D0 dissolved as fluxes J generated as integrated Poynting E = Q F1 + Q D0 Arbitrary Cross-section C in E 8 : (and charge densities) TS-Dualizing = `Helical’ String with Left-moving wave on it No net D2-brane charge but dipole q D2 » n D2 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. & Reall Bena & Warner Gauntlett & Gutowski T34Lift 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,  £ E 2 ( ,  )   r R  £ time = 5D black ring metric With 3 charges, each pair expands:

  r R  New feature: J   0 7 parameters: R, Q i, q i 5 conserved charges: Q i, J  and J  Infinite violation of uniqueness Choosing Q i, q i and J  as independent parameters:

Black String Limit Send R ! 1 keeping Q i / R and q i fixed Important: J  ! P   0 but J  ! 0 ! Black string solution of Bena  S2S2 12 M  M5 E B E £ B = 0 12 M  M5 E B E £ B / Q 1 q 1 + Q 2 q 2 + Q 3 q 3 – q 1 q 2 q 3 Suggests J  is Poynting-generated by SUGRA fields J  » s T 0  » s E £ B Components of D=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 & Papadopoulos Gauntlett, Lambert & West Problematic in open string description Circumvented in M-theory: Single M5-brane = Holomorphic 2-surface in T 6 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 T 6 S1S1 R 1,3 4D black hole Maldacena, Strominger & Witten; Vafa (0,4) CFT with c left = 6q 1 q 2 q 3 and left-moving momentum p p’ = p + M2-induced shift M-theory on T 6 £ S 1 £ R 1,3

Microscopic Entropy Counting Cyrier, Guica, D.M. & Strominger Single M5-brane = Holomorphic 2-surface in T 6 S 1 in R 1,4 5D black ring (0,4) CFT with c left = 6q 1 q 2 q 3 and left-moving momentum p = J  Counts states with J  =0 !!! M-theory on T 6 £ R 1,4

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 & Reall Bena & Kraus Same CFT describes Black Hole and Black Ring Decoupling limit:  ’ ! 0, r /  ’ fixed, etc. RG >