1. Density effect and beyond
Aspects of holography
July 14 (Mon), 2014 ~ July 23 (Wed), 2014
APCTP, Pohang, Korea
Holographic QCD:
Density effect and beyond 제목
Bum-Hoon Lee
Sogang University
Seoul, Korea

2. Contents I. Introduction – Motivation and Basics
String theory as a tool for the strongly interacting systems
II. AdS/QCD : the D7 in black D3/D-instanton geometry
III. Holographic meson mass splitting in the Nuclear Matter
IV. Holographic QCD : towards nonequilibrium
V. Summary

3. I. Introduction : Motivation & Basics
Q : How to understand the nonperturbative QCD, especially density dependence?
Ex1) confinement, chiral symmetry breaking,
phases (with or w/o chemical potential),
meson spectra etc. ?
Ex) How to understand the phenomena in the Strongly correlated condensed matter systems?
Strange metal
superconductor
Fermi
liquid
Pseudo
-gap
antiferromagnet
Temperature
Hole doping
Ex2) Nonequilibrium phenomena (such as heavy ion collision)?
AdS-CFT Holography : dim. QFT ⇔ 4+1 Classical Gravity Theory
Useful tool for strongly interacting systems,e.g., QCD, Condensed Matter, etc.

4. Holographic QCD - AdS/QCD
Goal : Using the 5 dim. dual gravity, study 4dim. QCD properties such as spectra & Phases (confining, deconfining, etc.), etc., in terms of
parameters (Nc, Nf, mq, T and μ, χ-symm., gluon condensation, etc.)
Needs the dual geometry of QCD.
Approaches :
Top-down Approach : rooted in string theory
Find brane config. or SUGRA solution giving
the gravity dual (May put the probe brane)
Ex) Nc of D3(D4) + M of D7(D8), 10D SUGRA
Sakai-Sugimoto Model, etc.
Bottom-up Approach:phenomenological
Introduce fields, etc. (as needed based on AdS/CFT)
5D setup → 4D effective Lagrangian
* Kaluza-Klein modes
– radial excitations of hadrons
* Confinement in Hard/Soft Wall Model
- by IR brane/dilaton running
Figure from Erdmenger et.al, EPJA(2008)

5. AdS/CFT Dictionary ( , ( , ) Partition function of bulk gravity
Witten 98; Gubser,Klebanov,Polyakov 98
Parameters
z= 1/u
boundary
( ,
( , )
Partition function of bulk gravity
bdry value of the bulk field
Generating functional of bdry QFT
: source of the bdry op.
: scalar  ,
Correlation functions by
5D bulk field  Operator
w/ 5D mass  w/ Operator dimesion
5D gauge symmetry  Current (global symmetry)
Radial coord. r in the bulk is proportional to the energy scale E of QFT

6. (Operator in QFT) <-> (p-form Field in 5D)
: Conformal dimension
: mass (squared)
Ex)
Gluon cond dilaton
baryon density vector w/ U(1)
fields in gravity
massless dilaton
scalar field with
m=0 vector field in the
gauge group
operators of QCD
gluon condensation
chiral condensation
mesons in the
flavor group
(or isospin group)
dual

7. AdS/CFT at finite temperature
(for the pure Yang-Mills theory without quark matters)
Witten ‘98
(thermal) AdS space(w/IR cutoff)
no stable AdS black hole
Low T (confining phase) : tAdS
QCD Phase
transition
Hawking-Page transition
at β(=1/Tc)
dual
=Transition of bulk geometry
2) High T (deconfining phase) : AdS BH
Schwarzschild AdS blackhole is stable

8. 2. Dual geometry for finite chemical potential
boundary
bulk
field
dual operator
( quark number density )
Chamblin-Emparan-Johnson-Myers,1999
Cvetic-Gubser,1999
5-dimensional action dual to the gauge theory with quark matters
Euclidean
Equations of motion
1) Einstein equation
2) Maxwell equation
Ansatz :

9. Solutions most general solution, which is RNAdS BH (RN AdS black hole)
S.-J. Sin, 2007
most general solution, which is RNAdS BH (RN AdS black hole)
black hole mass
black charge
quark chemical potential
corresponds to the deconfining phase (quark-gluon plasma)
quark number density
Note
The value of at the boundary ( ) corresponds to the
quark chemical potential of QCD.
2) The dual operator of is denoted by , which is the
quark (or baryon) number density operator.
3) We use

10. We call it tcAdS (thermal
What is the dual geometry of the confining (or hadronic) phase ?
find non-black hole solution
(BHL, Park ,Sin JHEP 0907,(2009))
baryonic chemical potential
We call it tcAdS (thermal
charged AdS space)
baryon number density
Note : Solutions in both phases are valid for arbitrary densities
Hawking-Page phase transition (in dense matter)
Phase : hadronic phase deconfined phase
Geometry: tcAdS ↔ RNAdS BH
(q = 0)
Geometry : thermal AdS ↔ AdS BH
(Geometries of Hawking-Page Tr. w/o chemical potential)

11. For the fixed chemical potential For the fixed number density
dimensionless variables
Legendre transformation,
the Hawking-Page transition occurs at

12. 1. Vector meson 2. Axial vector meson 3. pion
Light meson spectra in the hadronic phase
Jo, BHL, Park,Sin
JHEP 2010, arXiv:
Turn on the fluctuation in bulk corresponding the meson spectra in QCD
X is the dual to the quark bilinear operator <qbar q >.
1. Vector meson
2. Axial vector meson
3. pion

13. II. AdS/QCD based on the D7 embedding in black D3/D-instanton geometry
B. Gwak, M. Kim, BHL,Y.Seo,
S.-J. Sin, PRD86 (2012)
II. AdS/QCD based on the D7 embedding in black D3/D-instanton geometry
Motivation
Alternative to the Geometrical phase Transition for in AdS/CFT ?
Baryon Vertex (phase) and confinement at finite T (Black Hole Background) ?
Finite Temperature with Dilaton background
(Solution of Type IIB SUGRA)
Hawking Temperature
Zero Temperature Limit : becomes near horizon geometry of D3-D(-1)
(Liu & Tseytlin )
AdSxS5 at UV Flat at IR (w/ dilaton singular)
N=2 (with gluon condensation)

14. Ex) Zero Temperature and without density
AdSxS5 at UV
Flat at IR (w/
dilaton singular)
N=2 (with gluon
condensation)
Background Metric by D3 & D-instantons
(Liu & Tseytlin )
D7 Brane as a Probe
Induced metric on D7
DBI action of D7
becomes ( D7 wraps S3 of S5)
Rho->infty, AdS5xS3
Rho->0, rad (S3)->0
Embedding solution :

15. mq = 0
mq = 5
q = 0, 0.1, 0.3, 0.5, 1,3,5,10 from bottom to top

16. Ex) Finite Temperature and without density
Finite Temperature (Black Hole geometry) of D3/D-instanton system T
Quark-Gluon
Hadron
Rewrite in terms of dimensionless parameter or
where

17. Minkowski and Black Hole embedding
Induced metric on D7
DBI action of D7
Minkowski and Black Hole embedding
(from below)
‘Repulsion’ by q > ‘attraction’ by BH
Phase transition temperature
increases as q increases

19. Finite Temperature and with finite density
Turn on U(1) gauge field on D7 brane
DBI action of D7
Minkowski and Black Hole embedding

20. Quark Phase
Regularity condition
As q increases, the repulsion effect on D7 also increases.
F1 strings connect BH horizon and probe brane
Physical object is freely moving quark

21. In mq→ 0 limit, we have two phases
(Note : If q=0, then the trivial flat embedding is the unique solution for mq→ 0.)
Finite quark mass mq ≠ 0

22. Baryon Phase
F1’s connect spherical D5 & probe D7
Phys. Ob. = baryon vtx (bd state of Nc quarks)
χ-symm. broken
Background metric
Induced metric on D5
DBI action
D7 brane at the tip of D5 with force balance condition

24. Density dependence of free energy (for mq = 0 and q=15)
quark phase (χ –sym)
Baryon phase Q
quark phase (χ –broken)

25. Phase Diagram
Zero quark mass
Finite quark mass

26. III.Holographic meson mass splitting in the Nuclear Matter
BHL, S. Mamedov S. Nam, C. Park
JHEP 1308 (2013) 045
Nuclear medium in the hard wall model
action
flavor symmetry group
the thermal charged AdS (tcAdS) geometry (for confined phase)

27. the total nucleon number density
the grand potential defined in the grand canonical ensemble
gives
where
In the confining phase
the total nucleon number density
the density difference between proton and neutron

28. Light meson spectra in the nuclear medium
the vector fluctuations
the axial vector and pseudoscalar fluctuations

29. Vector mesons Take the Fourier mode expansion at the rest frame
the equations of motion for ρ-mesons or

30. The ρ-meson mass splitting
The a1-meson mass splitting
Pseudoscalar mesons
Binding energy of a heavy quarkonium

31. IV.Holographic Approach to the nonequilibrium physics
Two scenarios of
Far-from-equilibrium dynamics
Blue routes : Condensation Process
· Non-equilibrium evolution of an unstable configuration
Red routes: Quantum Quenching
· Dynamical response to a sudden
injection of energy
· Condensate undergoes an exponential growth
- Phase transition in “real” time !

32. Condensation Process on Anisotropic Background - evolution of scalar field
X. Bai, B-HL, M.Park, and K. Sunly arXiv:
Exponential growth!

33. Temperature
d dim. CMT
SC phase
Normal Phase
d+1 dim. Gravity
Black Hole with hair
Black Hole no hair

34. Quasinormal modes (QNMs) - linearized fluctuation
· Matching between QNMs (dashed) and
non-equilibrium evolution (solid)

35. V. Summary
QCD using Holographic dual Geometry - w/o chemical potential -
phase : confined phase ↔ deconfined phase transition
Geometry : thermal AdS ↔ AdS BH
Hawking-Page transition
Holographic QCD model in D3/D-instanton background
Two phases and phase transitions : for given T and density
quark phase : physical objects : quarks
baryon phase : baryon (vertex) as a physical object
We study phase structure with and without quark mass
We also study density dependence of chemical potential (eq. of state) and phase structure in grand canonical ensemble
Future works : Meson spectrum & beyond probe approximation, etc.

36. IV. Summary - continued
We also studied the nuclear and isospin density dependence of and phase structure in grand canonical ensemble.
Holographic principle can also be applied to the nonequilibrium physics
Holographic Principle may provide a new methodology
for the strongly interacting phenomena!

37. Thank You !