1 / 15

c-Theorem and Universal bound in AdS/ non -CFT correspondence

c-Theorem and Universal bound in AdS/ non -CFT correspondence. Based on arXiv:0804.0779. 溫文鈺 Wen-Yu Wen (NTU) 4/29/08 @ CYCU. Outline. Universal ratio in AdS/CFT Universal lower bound in AdS/ non -CFT Examples Proof by c-Theorem. AdS 5 / CFT 4 correspondence.

derora
Download Presentation

c-Theorem and Universal bound in AdS/ non -CFT correspondence

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. c-Theorem and Universal bound in AdS/non-CFT correspondence Based on arXiv:0804.0779 溫文鈺Wen-Yu Wen (NTU) 4/29/08 @ CYCU

  2. Outline • Universal ratio in AdS/CFT • Universal lower bound in AdS/non-CFT • Examples • Proof by c-Theorem

  3. AdS5/CFT4 correspondence • Consider N coincident D3 branes in IIB string • Open string degrees of freedom give rise to N=4 SU(N) super Yang-Mills theory in 3+1 dimensions • Field contents: gauge field Aμ, 6 scalars Xi, 4 fermions λa • R-symmetry SU(4) ~SO(6)

  4. AdS5/CFT4 correspondence • It was conjectured that same degrees of freedom are described by closed string (supergravity) on its (D3 branes’) near horizon geometry AdS5×S5

  5. AdS5/CFT4 correspondence • Dictionary of correspondence between operators (CFT) and states (Gravity) can be built.

  6. d-dimensional Conformal Field TheoryCentral charge • Cardy’s two-point function [correlator]: • This can also be calculated via boundary-boundary propagator of scalar field in AdS

  7. AdSd+1-BH/thermal CFTdEntropy density • Schwarzschild black hole in AdS • Bekenstein-Hawking

  8. Conjecture 1: Universal ratio • CFTs which admit a dual gravitational description via the AdS/CFT correspondence, the central charge is equal to the normalized entropy density (0801.2785:P.Kovtun,A.Ritz) • d=2 CFTs are always true due to symmetry regardless existence of gravity dual • This is a nontrivial claim for d > 2

  9. AdS/non-CFT • What happens to those non-CFT with gravitational dual description? • There appears additional scale(s) in field theory, set by non-trivial geometry or dilaton/scalar field in gravity side.

  10. Conjecture 2: Universal bound • Define c via correlator at short distance, therefore c is the same as before. • However, entropy density may be different. • We claim a lower bound by observing examples and prove by c-Theorem.[0804.0779:Wen]

  11. Example 1Hard-wall AdS/QCD Model • Hard IR cut-off in AdS, • Deconfinement phase transition set by • Entropy has been calculated [0705.1529:L.Pando Zayas]

  12. Example 2N=2* Pilch-Warner solution • Breaking N=4 to N=2 by introducing mass m to hypermultiplet, corresponding to two additional scalar fields with potential P • Entropy was calculated perturbatively at high T

  13. c-Theorem • Consider a general background with asymptotic AdS at infinity r (UV). • c-Theorem states that there exists a non-increasing function along the flow toward the IR. • This was proved by weak energy condition, saying [9904017:Freedman,Gubser,Warner]

  14. Proof for universal bound • Consider a multi-kink (Ki) geometry with AdS UV(IR) • Entropy is given in each kinkand • C-Theorem implies

  15. Thank You

More Related