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Multi-quark potential from AdS/QCD based 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. AdS 5 /CFT 4 -open string picture. - PowerPoint PPT Presentation
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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