1. Multi-quark potential from AdS/QCD based on arXiv:0708.2123 Wen-Yu Wen (NTU) @ Lattice QCD

2. OUTLINE AdS/(CFT,QFT,QCD) correspondence Light quark degree of freedom Heavy quark probe & sQGP Multi-quark potential Comments

3. AdS 5 /CFT 4 -open string picture N c D3 branes in IIB superstring Open strings excitation → SU(N c ) sYM 4 Gauge field in adjoint rep → Gluons of N c colors Dilaton decoupled → β=0, CFT 4

4. AdS 5 /CFT 4 - close string picture Superstring @ low energy limit ( l s → 0 ) → supergravity N c D3 brane has soliton-like metrics looks flat @ r → ∞ but AdS 5 ×S 5 @ r → 0 (near horizon limit) Isometry SU(2,2|4) agrees with sYM 4 r

5. AdS 5 /CFT 4 correspondence IIB superstring (supergravity) on AdS 5 xS 5 background is dual to N=4 SU(N c ) sYM (at large N c limit) (sYM) Usually large `t Hooft limit is taken: g→ 0, N c → ∞ s.t. λ=g 2 N c large (but finite) then only planar diagram is relevant, and non-planar ones become correction. (gravity) large λ=R 4 /α’ 2 assures that curvature is small and supergravity solution can be trusted.

6. AdS/QFT There are also correspondence between AdS 3 /CFT 2 (string@6D), AdS 4 /CFT 3 (M2 brane@11D), AdS 7 /CFT 6 (M5 brane@11D). For generic Dp-brane, dilaton cannot decouple and then β ≠ 0. We only have QFT.

7. AdS/QCD (AdS/CFT) sYM @ strong coupling regime is dual to supergravity @ weak curvature. (AdS/QFT) nontrivial dilaton plays role of running coupling. AdS 5 + dilaton ?/ QCD dilaton ~ 1/r 2 blows up @ IR and confinement was observed [soft-wall model] (O.Andreev,V.I.Zakharov;J.Erlich,D.T.Son,M.A.Stephanov) Confinement can be simply realized if IR part of AdS 5 is removed [hard-wall model] ( J.Erlich,D.T.Son,M.A.Stephanov )

8. Confinement the effective wall potential rises up at IR or cutoff r c Meson of small size → Coulomb potential thanks to conformal symmetry Meson of large size → linear potential thanks to IR wall r=0 r= ∞ IR

9. Deconfinement Finite temperature → AdS black hole; r H = 1/ π T Confinement phase @ r c > r H Deconfinement phase @ r c < r H IR Black Hole

10. Light quark degree of freedom Add N f flavor branes (D7), strings stretched between D3 and D7 represent quarks of fundamental rep. Strings on D7 represent meson degree of freedom. Usually assume N f << N c to ignore back reaction.

11. Heavy quark probe Quark mass is determined by integrating string tension from flavor brane to AdS center. Heavy quark is obtained by pushing D7 towards AdS boundary. Quark of infinite mass cannot be generated by finite- length string breaking, if no other dynamic (light) quark exists →quenched QCD

12. Heavy quark physics and sQGP Moving quark dumps energy into black hole → drag force ~ -√λ T 2 v/√1-v 2 Moving meson feels no drag force if size smaller than critical length. Jet quenching parameter can be calculated from light-like wilson loop. v

13. Heavy quark potential Wilson loop → string worldsheet S~ TE(L) for T >> L T L E(L) H.Boschi-Filho,N.R.F.Braga,C.N.Ferreira,06

14. Baryon vertex D5 wrapping on S 5 as baryon vertex, where Nc strings stick out. D5 tension cancels off Nc strings tension. Total energy is simply superposition of wrapped D5 and Nc strings. Without IR wall, E ~ 1/L

15. Baryon potential Insert IR wall, we obtain Cornell-like potential E ~ -A/L + σL + C A~√λ, σ~1/α’, C~R 5 /α’ Curve A: fit IR Curve B: fit UV Y-shape IR

16. Tetra-quark h L Tetra-quark potential: E~ -4A/L + (4L+h) σ + 2C Flip-flop @ small h: 4Q -> 2 mesons h L

17. Penta-quark and other exotic config. E~ -5A/L + (5L+h) σ + 3C In general, for exotic N quark, we may have E ~ -N A/L + (NL+h) σ + N C Naively, E is linear to total length. However deviation @ UV requires more thoughts, either flip-flop or attraction between vertices may contribute. h L

18. Finite-temperature String tension σ ~ √1-T 4 for small T However, lattice data expects σ decreases with T 2

19. comments Possible improvement on Cornell potential 1. UV perfection → string breaking (unquenched) 2. IR refinement → low transition T c 3. Incorporation of close string channel and flip- flop mechanism Correction due to finite N c ~ 10% Heavy-light configuration, i.e. Z(4430) Dynamics study

20. Thank You