Multi-quark potential from AdS/QCDbased on arXiv:0708.2123

Wen-Yu Wen (NTU)

@ Lattice QCD

OUTLINE

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

AdS5/CFT4 -open string picture

Nc D3 branes in IIB superstring Open strings excitation

→ SU(Nc) sYM4

Gauge field in adjoint rep → Gluons of Nc colors

Dilaton decoupled → β=0, CFT4

AdS5/CFT4- close string picture

Superstring @ low energy limit (ls → 0 )→ supergravity

Nc D3 brane has soliton-like metricslooks flat @ r →∞but AdS5×S5 @ r → 0 (near horizon limit)

Isometry SU(2,2|4)agrees with sYM4

r

AdS5/CFT4 correspondence

IIB superstring (supergravity) on AdS5xS5 background is dual to N=4 SU(Nc) sYM (at large Nc limit)

(sYM) Usually large `t Hooft limit is taken:g→0, Nc →∞ s.t. λ=g2Nc large (but finite)then only planar diagram is relevant, and non-planar ones become correction.

(gravity) large λ=R4/α’2 assures that curvature is small and supergravity solution can be trusted.

AdS/QFT

There are also correspondence between AdS3/CFT2(string@6D), AdS4/CFT3(M2 brane@11D), AdS7/CFT6(M5 brane@11D).

For generic Dp-brane, dilaton cannot decouple and then β ≠ 0. We only have QFT.

AdS/QCD

(AdS/CFT) sYM @ strong coupling regime is dual to supergravity @ weak curvature.

(AdS/QFT) nontrivial dilaton plays role of running coupling.

AdS5 + dilaton ?/ QCD dilaton ~ 1/r2 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 AdS5 is removed [hard-wall model](J.Erlich,D.T.Son,M.A.Stephanov)

Confinement

the effective wall potential rises up at IR or cutoff rc

Meson of small size→ Coulomb potential thanks to conformal symmetry

Meson of large size→ linear potential thanks to IR wall

r=0 r=∞

IR

IR

Deconfinement

Finite temperature→ AdS black hole; rH = 1/πT

Confinement phase @ rc > rH

Deconfinement phase @ rc < rH

IRBlack Hole

Light quark degree of freedom Add Nf flavor branes (D7), strings stretched between

D3 and D7 represent quarks of fundamental rep. Strings on D7 represent meson degree of freedom. Usually assume Nf << Nc

to ignore back reaction.

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

Heavy quark physics and sQGP Moving quark dumps energy into black hole

→ drag force ~ -√λ T2 v/√1-v2

Moving meson feels no drag force if size smaller than critical length.

Jet quenching parameter can be calculated from light-like wilson loop.

v

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

Baryon vertex

D5 wrapping on S5 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

Baryon potential Insert IR wall, we obtain Cornell-like potential

E ~ -A/L + σL + C A~√λ, σ~1/α’, C~R5/α’ Curve A: fit IR

Curve B: fit UV

Y-shape

IR

Tetra-quark

h

L

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

h

L

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

Finite-temperature

String tension σ ~ √1-T4 for small T However, lattice data expects σ decreases

with T2

comments

Possible improvement on Cornell potential1. UV perfection → string breaking (unquenched) 2. IR refinement → low transition Tc3. Incorporation of close string channel and flip-flop mechanism

Correction due to finite Nc ~ 10% Heavy-light configuration, i.e. Z(4430) Dynamics study

Thank You