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Dynamical Holographic QCD Model
Mei HUANG
Institute of High Energy Physics, CAS
Theoretical Physics Center for Science Facilities, CAS
Seminar at USTC, Oct.10, 2013
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I. Why hQCD ? From UV to IRII. Pure gluon system: Quenched dynamical hQCD Glueball spectra III. Two flavor system: Dynamical hQCD Meson spectra Decay constant and form factorIV. Phase transitionsV. Conclusion and discussion
Danning Li, Mei Huang, arXiv:1303.6929Systematic framework for chiral symmetry breaking & confinement
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I. Why hQCD ? From UV to IR
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QCDUV (Weak coupling):
Asymptotic freedom
Asymptotically conformal
IR (Strong coupling):
Chiral symmetry breaking
& Confinement
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Strong QCD
Quarks & Gluons (UV)
QM, NJL, SM, HLS,
CHPT, NRQCD……
DSE
color flux tube
Dual superconductor …Holographic QCD (hQCD)
Effective field theories and models
Lattice QCD
Vacuum(IR)
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Quantum GravityStrongly Coupled Gauge Theory
Holographic Duality: Gravity/QFT
General Gravity/QFT:
AdS/CFT : Original discovery of duality
Supersymmetry and conformality are required for AdS/CFT.
In general, supersymmetry and conformality are not necessary
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Holographic Duality: (d+1)-Gravity/ (d)-QFT
Holography & Emergent critical phenomena:
When system is strongly coupled, new weakly-coupled degrees of freedom dynamically emerge.
The emergent fields live in a dynamical spacetime with an extra spatial dimension.
The extra dimension plays the role of energy scale in QFT, with motion along the extra dimension representing a change of scale, or renormalization group (RG) flow.
arXiv:1205.5180
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Holographic Duality & RG flow
Coarse graining spins on a lattice: Kadanoff and Wilson
arXiv:1205.5180
J(x): coupling constant or source for the operator
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Holographic Duality & RG flow
QFT on lattice equivalent to RG problem from Gravity
RG scale -> an extra spatial dimension Coupling constant -> dynamical filed
arXiv:1205.5180
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Holographic Duality: Dictionary
Boundary QFT Bulk Gravity Local operator Bulk field
Strongly coupled Semi-classical
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holographic QCD (5D)
Real QCD world: Rich experimental data and lattice data
3rd step: gravity dual systematic framework
2nd step: deformed AdS5
intelligent guess
1st step: just AdS5
naïve try
Build the connection between QCD dynamics and geometry
Holographic QCD or gravity dual of QCD
String theorists’ business: whether it can be deduced from 10D string theory ?
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QCD nonconformal
N=4 Super YM conformal
AdS5deformed AdS5
Dilaton field breaks conformal symmetry
A systematic framework: Graviton-dilaton system
Input: QCD dynamics at IRSolve: Metric structure, dilaton potential
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Dynamical hQCD & RG
A AdS5
deformed AdS5
QCD Dynamics at IR
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II. Pure gluon system: quenched dynamical hQCD
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5D action: graviton-dilaton
Pure gluon system:
Gluon condensate at IR:
dual to
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Graviton-dilaton system
A AdS5
deformed AdS5
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Glueball spectra:
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5D action for scalar glueball:
scalar glueball: dual to
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1) Dimension-4 dilaton field
No linear Regge behavior
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2) Soft-wall model with AdS5 metric (“KKSS”)
Cannot accommodate the ground state and the linear slope!
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3) Selfconsistent dimension-2 dilaton field
Surprise!No extra parameter!
deformed metric
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4) Dilaton field: quartic at UV and quadratic at IR
However, the dual gluon operator of dimension-2 dilaton field is not known!
Gauge invariant & Local operator
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Not sensitive to quartic form at UV.Determined by quadratic form at IR.
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Linear confinement
Confinement potential
Q Q
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1, AdS5 only gives Coulomb potential ! 2, Deformed metric structure is needed to produce the linear potential!
Holographic dictionary:
Metric structure determines the quark potential !
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Criteria for linear potential
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III. Two flavor system: Dynamical hQCD & Meson spectra
Add flavor dynamics on gluodynamic background
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Deformed AdS5 models for hadron spectra:
hard-wall AdS5 model soft-wall AdS5 model: quadratic dilaton model 1, Hard-wall AdS5 model:
5D hadron action
AdS5 metric
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Lowest excitations: 80-90% agreement
However, no Regge behavior in the hard-wall AdS5 model !
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A dilaton field to restore Regge behavior
2, Soft-wall AdS5 model or KKSS model
However: only Coulomb potential, no linear quark potential
AdS5 metric
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Degeneration of chiral partners in KKSS model
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3, Modify action by a quartic interaction T. Gherghetta, J. I. Kapusta and T. M. Kelley, Phys.Rev. D 79 (2009) 076003; T. M. Kelley, S. P. Bartz and J. I. Kapusta, Phys. Rev. D 83 (2011) 016002;
Negative mass squarefor scalar meson: instability
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4, Modify metric Yanqin Sui, Yueliang Wu,Yibo Yang, Zhifeng Xie, arXiv:0909.3887, PRD2010; Yanqin Sui, Yueliang Wu,Yibo Yang, arXiv:1012.3518, PRD2011 ……
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How to realize
chiral symmetry breaking,
& linear Regge behavior
& linear quark potential
in a unified model?
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Graviton-dilaton-scalar coupling system
Action for pure gluon system: Graviton-dilaton coupling
Action for light hadrons: KKSS model
Total action:
D.N. Li, M.H., arXiv:1303.6929
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Background with gluon condensate and quark-antiquark condensate
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Graviton-dilaton-scalar system
A AdS5
deformed AdS5
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IR asymptotic form constrained by linear potential:
UV asymptotic form:
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Chiral fieldDilaton field
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Produced hadron spectra compared with data
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Produced hadron spectra compared with data
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Regge behavior and linear quark potential
Linear confinement
String model & confinementq q
Flux tubes of color field = glue
QCD and string theory I:
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Solved Metric Produced quark potentialcompared with Cornell potential
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Decay Constant and Form Factor
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Smaller chiral condensate, smaller pion decay constant,
better pion form factor
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large chiral condensate, better pion decay constant,
worse pion form factor
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HQCD for
Phase transitions
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5D graviton action:
Metric structure, blackhole, Dilaton field and Dilaton potential should be solved self-consistently from the Einstein equations.
Color electric deconfinement phase transition
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Experiences in constructing holographic QCD model tells us that: a quadratic correction in the deformed warp factor is responsible for the linear confinement.
D.N, Li, S. He, M. H., Q. S. Yan, arXiv:1103.5389, JHEP2011
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Indeed, the positive quadratic correction dAdS5 model can fit all the finite temperature lattice QCD data for pure gauge SU(3) theory.
D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011
53D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011
54D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011
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Trace anomaly
D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011
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Heavy quark potentialElectric screening
Polyakov loop: color electric deconfinement
D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011
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spatial Wilson loop spatial string tension
Magnetic screening and magnetic confinement
D.N. Li, S. He, M.H., Q. S. Yan, arXiv:1103.5389, JHEP2011
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V. Conclusion and discussion
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1, A systematic framework connecting QCD dynamics and geometry:
graviton-dilaton for pure gluon system graviton-dilaton-scalar for hadron spectra
2, The linear Regge behavior as well as linear quark potential can be produced in a dynamical holographic model! The dimension-2 dilaton field at IR induces the linear confinement.
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3. We have realized chiral symmetry breaking,
& linear Regge behavior & linear quark potential
in a unified model!
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4. Dynamical hQCD & RG
A AdS5
deformed AdS5
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Outlook
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Strong QCD
Quarks & Gluons (UV)
QM, NJL, SM, HLS,
CHPT, NRQCD……
DSE
color flux tube
Dual superconductor …Holographic QCD (hQCD)
Effective field theories and models
Lattice QCD
Vacuum(IR)
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Light flavor Hadron spectra
Ground states:
Effective models
Excitation states:
hQCD models
Easy Easy
Hard Easy
Heavy flavor Hadron spectra?
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Phase structure
Chiral restoration
Effective models
Deconfinement
hQCD models
Easy Not easy
Easy Hard
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Hard for
Effective QCD
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Easy for
hQCD
But we need a hQCD close to QCD!
Dynamical hQCD model is one of the candidates!
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Thanks for your attention!
