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Domain-wall/QFT correspondence

Domain-wall/QFT correspondence. A Bridge Connecting Gravity and Gauge Theory. Wen-Yu Wen Academia Sinica Feb 24, 2006. Outline. Holographic Principle AdS/CFT correspondence D-brane: open/closed string duality DW/QFT correspondence Applications. Holographic Principle.

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Domain-wall/QFT correspondence

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  1. Domain-wall/QFT correspondence A Bridge Connecting Gravity and Gauge Theory Wen-Yu Wen Academia Sinica Feb 24, 2006

  2. Outline • Holographic Principle • AdS/CFT correspondence • D-brane: open/closed string duality • DW/QFT correspondence • Applications

  3. Holographic Principle • GR: inevitable existence of black holes • After formation of BH, the entropy is proportional to the area of event horizon [Bekenstein-Hawking] S=1/4 A

  4. Holographic Principle • Holographic Principle: the universe is really a hologram which is isomorphic to the information "inscribed" on its boundaries… [‘tHooft 93; Susskind 94] • A gravitational theory should be related to a non-gravitational theory in one fewer dimension. What's inside?

  5. g g gluon SU(3) AdS/CFT correspondence U(1) Start with 4d gauge theories with some additional properties: • Large Nc [‘tHooft 02] • Strong coupling λ = g2Nc • Supersymmetry N = 4 This may still serve a good approximation of QCD Electrodynamics photon g g electron Chromodynamics 3 colors (charges)

  6. AdS/CFT correspondence Now we have N=4 SU(Nc) SCFT • Scale invariant: β(μ)=0 • Symmetry group: Poincar`e + scaling + others SO(4,2)~SU(2,2) • 4 supercharge rotated by R-symmetry SU(4)~SO(6) 1 gauge field Aμ 4 Weyl fermions ψa 6 real scalars φi • These make superconformal group SU(2,2|4) • S-duality [Montonen-Olive] SL(2,Z)

  7. AdS/CFT correspondence Can it also be described by an effective (gravitational) theory in 5d? (Holographic principle) • If the 5th coordinate associates with energy scale in CFT… This is exactly a 5d anti-de Sitter (AdS) space (Poincar`e patch). R4 AdS5 ∞ 0 r infrared, low energies ultraviolet, high energies Boundary

  8. AdS5 x S5 Isometry of AdS SO(4,2) Isometry of S SO(6) IIB N=8 susy Gravitons Mass of particles CFT4 Conformal groupSO(4,2) R-symmetrySU(4) N=4 linear +4 conformal Energy stress tensor Scaling dimension AdS/CFT correspondence In fact, we need 5 more spatial dimensions… 10d type IIB supergravity in AdS5 x S5 More than that, we need IIB superstring!

  9. N=4 SYM on M4 gs=gYM2 Large λ, large Nc Finite λ, large Nc Finite λ, finite Nc IIB on AdS5 x S5 l4 =4πgsNcα’2 Classical SUGRA Classical string Full quantum string AdS/CFT correspondence Three forms of correspondence with increasing strength: [Maldacena, Witten, Gubser, Klebanov, Polyakov]

  10. Applications • Regulate mass of dilatonic black hole [Michael Duff, James Liu, et al ‘99] by Hamilton-Jacobi counterterms [Wen, Liu, et al. ‘04] • Construct AdS5[Lin, Lunin, Maldacena] and AdS3 bubbles solution [Wen, Liu, Vaman ‘05] • Generalize to DW/QFT correspondence in null-like background [Wen, Lin; Ho, Chu ‘06]

  11. D-brane physics • AdS/CFT is one realization of gravity/gauge field • In term of string theory, this is open/closed string duality • D-brane plays an essential role[Polchinski ‘95]

  12. D-brane physics • As a SUGRA solution, Dp-brane interpolates between flat Minkowski and AdSxS geometry. • Dilaton decouples only for p=3 , where AdS/CFT is applicable. R1,9 AdSp+2 x S8-p

  13. Domain-Wall solutions • Low energy limitkeep fixed • Fixed `tHooft coupling let • Weyl transforms metric to “dual frame” [Boonstra,Skenderis,Townsend;Itzhaki,Maldacena ‘98] Wall as a probe brane P<3 P>3

  14. Null-like DW/QFT • Functions a,b,h need to satisfy equations of motion • Solution preserves ¼ BPS • Geodesic is not complete • X+ is a Killing direction, can be seen as (light-cone) “time”

  15. Probing DW solution • This DW background can be probed by a test brane • There are two ways, which give slightly different energy-distance relation: • Open string stretching in between • Closed string propagates Nc-1

  16. QFT living on the wall • DBI action of “wall” = action of SU(Nc) QFT • Effective coupling is running with U and x+ • Gravity/gauge theory are only valid in certain regimes: • Classical gravity is good at large geff and small dilaton • Perturbative gauge theory is good at small geff

  17. Boundary Cosmology • rewrite equation of motion for a(x+), where P, Q are related to h. • Two simple solutions: • P=Q=0 • P=0, Q=const • Boundary theory valids at E > H

  18. References • related papers by authors mentioned in this talk, especially • Bubbling 1/4 BPS solutions in type IIB and supergravity reduction on Sn x Sn [Wen, Liu, Vaman; 0412043] • Black hole mass and Hamilton-Jacobi counterterms [Wen,Batrachenko,Liu,McNees,Sabra; JHEP 0505 (2005) 034] • Supersymmetric null-like holographic cosmologies [Wen,Lin; 0602124] • some pictures are taken from online resources, such as Scientific American, Wikipedia, NOVA, etc.

  19. Thank You

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