Supertubes Supersymmetric Black Black Rings Rings Supertubes - PowerPoint PPT Presentation

Supertubes Supersymmetric Black Black Rings Rings Supertubes Supersymmetric and and S 2 S 1 David Mateos Mateos David

• 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 S 1 × × S 2 × × S 2 S 1 flat directions = Black Supertube × × × ×

Why are Black Rings interesting? D=5: Black Ring D=4 M, Q, J, … M, J, Q 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 1/4-SUSY preserved C C C C Q F1 and Q D0 dissolved as fluxes J generated as integrated Poynting E = Q F1 + Q D0 E F1 J C in � � 8 : � � Arbitrary Cross-section C C C D0 (and charge densities) P B TS-Dualizing = `Helical’ String with Left-moving wave on it P Tubular D2/F1/D0 J ¼-SUSY Bound State No net D2-brane charge but dipole q D2 ∼ ∼ n D2 ∼ ∼

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

Elvang, Emparan, DM & Reall 3-charge Supertubes and Supersymmetric Black Rings: Bena & Warner Supergravity Description Gauntlett & Gutowski Ring solution with regular horizon → → → → 3 charges Best microscopic description → → → → M-theory First, lift 2-charge supertube to M-theory: T34 Lift ρ ρ ρ ρ With 3 charges, each pair expands: φ R r ψ ψ ψ ψ � 4 = � 2 (r, ψ) × � 2 ( ρ , φ ) � 6 × time = 5D black ring metric

ρ ρ ρ ρ φ New feature: J φ ≠ 0 φ ≠ ≠ ≠ φ φ R 7 parameters: R, Q i , q i r ψ ψ ψ ψ 5 conserved charges: Q i , J ψ ψ and J φ ψ ψ φ φ φ Infinite violation of uniqueness by 2 continuous parameters Choosing Q i , q i and J ψ ψ as independent parameters: ψ ψ

Black String Limit Send R → → → → ∞ ∞ ∞ ∞ keeping Q i / R and q i fixed Black string solution of Bena Important: J ψ ψ → → → P ψ → ≠ 0 but J φ φ → → 0 ! → → ψ ≠ ≠ ≠ ψ ψ ψ ψ φ φ ψ S 2 φ ∼ ∼ ∼ ∼ ∫ ∫ ∫ T 0 φ ∫ φ ∼ ∼ ∫ ∼ ∼ ∫ ∫ E × ∫ × × × B J φ Suggests J φ φ is Poynting-generated by SUGRA fields φ φ φ φ φ φ 12 12 M2 M2 3456 ψ 3456 ψ Components of E E B B D=11 SUGRA F 4 M5 M5 E × × B = 0 × × E × × × × B ∝ ∝ ∝ ∝ Q 1 q 1 + Q 2 q 2 + Q 3 q 3 – q 1 q 2 q 3

Worldvolume 3-charge Supertubes First step: F1/D4/D0 bound state with D2/D6/NS5 dipoles Bena & Kraus Circumvented in M-theory: Problematic in open string description 7 C Gibbons & Papadopoulos Gauntlett, Lambert & West Single M5-brane = Elvang, Emparan, D.M. & Reall Holomorphic 2-surface in � � 6 � � Turning on H induces M2 charge and allows arbitrary C In summary: Captures 3 dipoles, J φ φ = 0 φ φ

Microscopic Entropy Counting Maldacena, Strominger & Witten; Vafa M-theory on � � 6 � 1,3 � � � � � × × × × S 1 × × × × Single M5-brane = � 1,3 � � � Holomorphic 2-surface in � � � 6 � S 1 4D black hole (0,4) CFT with c left = 6q 1 q 2 q 3 and left-moving momentum p p’ = p + M2-induced shift + zero-point shift

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

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

MESSAGE MESSAGE = Supersymmetric Black Black Rings Rings Supertubes Supertubes Supersymmetric S 2 S 1