Flavor quark at high temperature from a holographic Model Ghoroku (Fukuoka Institute of Technology) Sakaguchi (Kyushu University) Uekusa (Kyushu University) Yahiro (Kyushu University) Hep-th/0502088 (Phys.Rev.D71:106002,2005 )
Contents 1. Introduction 2. Finite-T Supergravity solution with non-trivial dilation 3. A brief overview of phase diagram 4. Chiral symmetry by using D7 brane; probe approximation is taken. 5. Confinement/deconfinement phase transition by using the fundamental string 6. T dependence of meson mass by using the potential between quark and anti-quark and also by fluctuation of D7 brane. 7. T dependence of baryon mass by using D5 brane 8. Summary
Holograph (Gauge/Gravity correspondence) J. Maldacena, Adv. Theor. Phys. 2 231(1998) AdS 5 S 5 correspondence CFT(N=4 SYM) Top-down Chiral symmetry breaking Insertion of flavor brane Bottom-up Erlich,Katz,Son,Stephanov Da Rold, Pomarol Teramond, Brodsky Erdmenger,Evans,Grobe Background? correspondence QCD etc Successful in explaining basic properties of light mesons Gravity side Gauge theory side
The holographic dual of a finite-t gauge theory AdS-Schwarzschild correspondence CFT plasma Top-down Background with non-trivial dilaton Bottom-up Ghoroku and Yahiro? Gravity side correspondence QCD plasma Gauge theory side
(T=0) N=1 gauge theory q the gauge field condensate
Supergravity solution at finite T: D3 r Thermal system with running coupling constant in the gauge theory side.
A brief overview of phase diagram described by the dual gauge theory N=1 supersymmetry Chiral symmetry Confinement Chiral symmetry Deconfinement Ghoroku and Yahiro hep-th/040804 T=0 T=T fund T Confinement/deconfinement phase transition dc/dt, de/dt T Real QCD T~160 MeV Chiral symmetry is restored. deconfinement
Chiral symmetry Karch-Katz;hep-th/0205236, Evans-Shock;hep-th/0403279, Kruczenski et al.;hep-th/0304032 D3 X1,X2,X3 ρ D7 X1,X2,X3 X4,X5X,6,X7 X8,X9 Probe approximation is taken here. The basic geometry of the D3-D7 system
Insertion of D7 brane (X4,X5,X6,X7,X8,X9) part of metric ρ D7 X8,X9
Induced metric for D7 brane X9 X8 The D7 brane action The eight form potential Hodge dual to the axion
Set, X9 X8 Hodge dual field strength of Gibbons, Green and Perry Equation of motion for where, and the b.c. is
The asymptotic form of at large r ( large ρ) is the quark mass, is the chiral condensate, since the conformal dimension of the CFT operator corresponding to is three.
In the case of the AdS limit (q=0) The same phase transition takes place by changing m with T fixed reported by Babington, Erdmenger, Evans, Guralnik and Kirsch.
In the case of non-trivial dilation with finite q attractive force by
Opposite to the case of spontaneous chiral symmetry breaking in QCD The AdS case T=T fund Chiral symmetry is preserved
Temperature dependence of D7 brane energy Regularized energy
T=Tfund
A brief summary on chiral symmetry Chiral symmetry is preserved. Phase transition T=0 T=T fund C and E are not smooth. T
Confinement or deconfinement Wilson-Polyakov loop String world-sheet Gravity side The Nambu-Goto action The induced metric
Parallel strings Parallel string configuration D3 D7-brane S 5 r r=σ
Dynamical quark mass Energy of parallel strings D3 D7-brane r
Temperature dependence of dynamical quark mass Lattice simulation (Kaczmarek et al.) Witten s non-susy black-hole solution which dominates at high temperatures
U-shaped string The U-shaped configuration D7 D3 r r(σ) r 0 2L X1=σ
Nambu-Goto Lagrangian Equation of motion for
Potential between quark and anti-quark Energy of string Distance between quark and anti-quark D7 D3 r r(σ) r 0 2L X1=σ
Potential between quark and anti-quark q q L q _ r D3 D7 AdS(q=0) Finite q
q L Possible meson spectrum _ q Lattice calculation O. Kaczmarker, S. Ejiri, F. Karsch, E. Laermann and F. Zantow, hep-lat/0312015
When T=T fund D7 D3 r r(σ) r 0 2L X1=σ
The D7 brane action Fluctuation of D7 brane
Temperature dependence of meson mass q L _ q T=T fund
Lattice simulation for J/ψ J/ψ(3 GeV) Maximal Entropy Method Asakawa & Hatsuda, PRL 92 ( 04) 012001 32 3 x (32-96)
Baryon mass D7 The action of D5 brane D5-brane S 5 The induced metric r D3 D5 coordinate The baryon mass function
T=0 T>0 T=0 D5-brane S 5 T=0.15 r T=0.2 T=0.26 D3 r T
Summary 1. We constructed the finite-temperature background with non-trivial dilation. 2. The background well simulates several properties of QCD above T c of the confinement/deconfinement phase transition. a) Chiral symmetry b) deconfinement 3. The present theory shows another phase transition at T= T fund.
Summary(2) Confinement/deconfinement phase transition q L q q _ T c =0 Meson, baryon T=T fund V=0 T Meson, baryon Quark-gluon plasma T Real QCD T~160 MeV Chiral symmetry, deconfinement