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Microscopic Entropy of Black Rings Trobada de Nadal 2004 a ECM

S 2. S 1. Microscopic Entropy of Black Rings Trobada de Nadal 2004 a ECM. David 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

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Microscopic Entropy of Black Rings Trobada de Nadal 2004 a ECM

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  1. S2 S1 Microscopic Entropy of Black Rings Trobada de Nadal 2004 a ECM David Mateos

  2. 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

  3. Black Ring = Asymptotically Flat, Stationary Black Hole Solution in 5D with Horizon Topology S1£ S2 S2 S1 £ flat directions = BlackSupertube

  4. 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

  5. E P F1 J D0 P Tubular D2/F1/D0 Bound State J B 2-charge Supertubes: Worldvolume Description D.M. & Townsend Supersymmetric Brane Expansion in Flat Space by Angular Momentum 1/4-SUSY preserved QF1 and QD0 dissolved as fluxes J generated as integrated Poynting E = 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 C ¼-SUSY

  6. Easily understood ~ D2/anti-D2 pair: 2-charge Supertubes: Supergravity Description Emparan, D.M. & Townsend No net D2 charge, but D2 dipole (and higher) moments: x

  7.  R r  T6 E4 = E2 (r, ) £E2 (,  ) First, lift 2-charge supertube to M-theory: T34 Lift With 3 charges, each pair expands: 3-charge Supertubes and Supersymmetric Black Rings: Supergravity Description Elvang, Emparan, D.M. & Reall Bena & Warner Gauntlett & Gutowski Ring solution with regular horizon ! 3 charges Best microscopic description ! M-theory £ time = 5D black ring metric

  8.  R r  Infinite violation of uniqueness New feature:J 0 7 parameters: R, Qi , qi 5 conserved charges: Qi , J and J Choosing Qi, qi and J as independent parameters:

  9. Black string solution of Bena  S2 J»s T0»s E £ B Suggests J is Poynting-generated by SUGRA fields 12 12 M2 M2 3456 3456 Components of D=11 SUGRA F4 E E B B M5 M5 E £ B = 0 E £ B / Q1 q1 + Q2 q2 + Q3 q3 – q1 q2 q3 Black String Limit Send R !1 keeping Qi / R and qi fixed Important: J! P 0 but J! 0 !

  10. First step: F1/D4/D0 bound state with D2/D6/NS5 dipoles Bena & Kraus Problematic in open string description 7 Holomorphic 2-surface in T6 Worldvolume 3-charge Supertubes Circumvented in M-theory: C Gibbons & Papadopoulos Gauntlett, Lambert & West Single M5-brane = Elvang, Emparan, D.M. & Reall Turning on H induces M2 charge and allows arbitrary C In summary: Captures 3 dipoles, J = 0

  11. Single M5-brane = S1 R1,3 4D black hole Holomorphic 2-surface in T6 (0,4) CFT with cleft= 6q1q2q3 and left-moving momentum p Microscopic Entropy Counting Maldacena, Strominger & Witten; Vafa M-theory on T6£ S1£R1,3 p’ = p + M2-induced shift

  12. Single M5-brane = S1in R1,4 5D black ring Holomorphic 2-surface in T6 (0,4) CFT with cleft= 6q1q2q3 and left-moving momentum p = J Counts states with J=0 !!! Microscopic Entropy Counting Cyrier, Guica, D.M. & Strominger M-theory on T6£R1,4

  13. One conclusion: Microscopic constituents of Susy Black Rings = Supertubes One open question: Microscopic versus macroscopic descriptions? or J ?

  14. Decoupling limit: ’ ! 0 , r /’ fixed, etc. RG > Same CFT describes Black Hole and Black Ring 3-charge Supertubes D1/D5/P System Elvang, Emparan, D.M & Reall Bena & Kraus

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