Baryons and Vector Dominance in Holographic Dual QCD

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Baryons and Vector Dominance in Holographic Dual
QCD
NFQCD08 Kyoto

• Towards Hot and Dense Matter

Mannque Rho IPhT, CEA Saclay
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Role of Holographic Duality in QCD
Two basically different attitudes

• Interested in how well string theory, TOE with
  its humongous universes , can reproduce QCD in
  our universe a facet of well established
  Nature Postdiction of the knowns.
• Interested in describing the unknowns that are
  difficult to access by QCD but might be possible
  by string theory, i.e. AdS/CFT.

String theorists
This Talk
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Based on works with or by
G.E. Brown, M. Harada, D.-K. Hong, C.-H. Lee,
B.-Y. Park, C. Sasaki, H.-U. Yee P. Yi
Goal
Hidden gauge symmetric description of whats
going on in hot and/or dense matter
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Key Point
Non-perturbative strong interaction phenomena at
E ltlt L can be encapsulated in 5D YM
Chern-Simons action.
SCS ,
U(N) Hidden local symmetry (HLS)

• (1) Bottom-up emergence? emergent HLS
• (2) Top-down reduction ? reduction HLS

In 4D, S consists of Goldstone pions and an
Infinite tower of hidden local gauge fields.
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Bottom-Up
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Emergence
? Weinbergs folk theorem

• At E 0 , Soft pion/current algebra

• U invariant under

Hidden local symmetry emerging gauge fields r,
w ? HLS1
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HLS1 a la Harada-Yamawaki
Harada and Yamawaki 2001

• HLS1 Lagrangian in the chiral limit 3
  parameters
• g (gauge coupling), Fp and Fs or (g, Fp , a
  (Fs/Fp)2)

- (1/2g2) trrmnrmn
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Dimensional deconstruction
Bring in a tower of vector mesons as emergent
gauge fields. Moose construction
Georgi et al. 1999

• Harada-Yamawaki rewritten

k0
a 1
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• Two vector mesons

• Many (K?) vector mesons in open moose

HLS?
4D gauge theory on lattice
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And take continuum limit with K ?, e?0 ? 5D YM

• The pion field appears as a Wilson line

Atiyah-Manton 1989

• Extension in 5th dimension, i.e., dimensional
• deconstruction via infinite tower of vector
  mesons
• which are encapsulated in YM fields in warped
  metric.

• Global chiral symmetry in 4D is elevated to a
  local
• gauge symmetry in 5D

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The resulting theory, ultraviolet completed to
QCD, is dimensionally deconstructed QCD
Son/Stephanov 2004
Low-energy QCD

• infinite tower of hidden local gauge fields
• baryons are instantons in 5D YM theory.

Weinbergs folk theorem
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Top-Down
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Gauge/Gravity Correspondence
Sugimoto, String 06
In general relativity, a (heavy) particle is
represented as a curved background
Solution of Einstein Eq
dual !
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Holographic QCD
Sakai and Sugimoto 2005

• AdS/CFT strategy
• Strings and D4 (color Nc), D8/D8 (flavor Nf)

• Break SUSY completely ? Nc D4 branes
• wrapped on S1 with BC ? U(Nc) gauge theory
• applicable for EltltL
• Add Nf D8-D8 brane pairs to the D4 system
• ? U(Nc) QCD with Nf massless quarks ?
• flavor gauge symmetry U(Nf)xU(Nf)
• Replace D4 by SUGRA solution and break
• gauge U(Nf)xU(Nf) ? U(Nf) in 5D -- which in
  4D
• corresponds to global chiral symmetry
  breaking

Valid for quenched approx NfltltNc
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Strictly valid for

• Large lgYM2 Nc
• Eltlt MKK
• Large Nc
• Nc gtgt Nf
• mq 0

Supergravity approximation
Scale of 5th dimensiopn
Probe approximation
Chiral limit
Quenched approximation in the chiral limit
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5D HLS
Sakai Sugimoto 05
D8 branes in D4 background
Supergravity solution, Change of variables,
KK
5D YM
Chern-Simons Anomaly term
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Infinite Tower
Sakai Sugimoto 05
Mode expand
Eqs. of motion
HLS?
SD8 for infinite tower of vector mesons coupled
to Goldstone pions with the chiral symmetry of
QCD
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Baryons
Where are the baryons?
To answer, note Wittens baryon vertex (wrapped
D4 on S4) dissolves into D8 branes
D4
D8
Nc
D8
Therefore baryons must appear in 5D YM theory as
instantons
or In 4D as skyrmions embedded in infinite tower
of vector mesons
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What Came Out
Hong, Rho, Yee, Yi, Dynamics of baryons from
string theory and VD,
JHEP 09 (2007) 063
Agree with quenched lattice results
First derivation!
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Here comes something new!

• In 5D, in the large t Hooft limit, the baryon is
  tiny, R? 9.6/MKKl1/2 ? 0 . Basis for baryon
  chiral perturbation theory with systematic 1/l
  and 1/Nc corrections ? Nuclear physics a la
  Yukawa.
• EW response is totally vector-dominated, i.e.
  form factors for p, r, w, with the infinite
  tower.

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Vector Dominance
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Old Vector Dominance
All hadron form factors are vector
dominated with the ground-state vector mesons (r,
w, f)
Sakurai 1969
p
g
p
Sakurai
0
?
Fp (q2)
?
?
?
?
?
?
?
?
?
?
?
?
?
q2 (GeV2)
(q2)1/2
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New VD with infinite tower
Sakai Sugimoto 2005
It works well!
e.g. charge radius
SS model
Experiment
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Baryon is a different story
There is a point-like instanton configuration
? Expect
rk

Deviation from VD
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What nature says
With the ground state vector mesons r w only
Sakurais old VD does not work for the nucleon
Fit
(Asymptotic form factor with c(0)1 given by
perturbative QCD)
A good fit is obtained to k2 ? 1 GeV2 with a
1.02
Bijker and Iachello 2004
Vector dominance is maximally violated
for the nucleon and nuclei!!
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Bijker-Iachello Fit a1.02
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New VD Holographic duality acts
Point-like instanton gets absorbed into the tower
EW fields appear as boundary conditions of 5D
bulk gauge field, i.e.
Proof
And the gauge field represents normalizable modes
in 5D
QED

• Vector dominated with ? tower
• Sum rule

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Predictions

• Charge sum rule
• Universality
• Radii

Cf Sakurai
EXP
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Presents
A totally new perspective on topological
structure of baryons and dense baryonic matter

• BR scaling
• Dileptons
• Kaon condensation
• Skymion-half-skyrmion transition
• Instanton-meron transition
• CFL
• Compact star structure
• Etc.

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But we dont know how to apply the theory to
hot/dense matter

• Doing 1/Nc and 1/l corrections in gauge sector ?
  Loop and a corrections in string sector is
  unknown. Without them, no temperature/density
  dependence in meson mass or quark condensate in
  the confinement regime.
• Current quark masses difficult to implement
  perhaps need tachyon condensation etc. which
  seems to give GMOR formula correctly, but unknown
  whether it is correct or unique or useful.
• Putting baryonic density seems harder than
  temperature. For instance, even pion decay
  constant in nuclear medium does not come out
  reasonably.

Await resolution by bright string theorists
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Can-do approach truncate the tower ?dualHLS1
Harada, Matsuzaki and Yamawaki showed (2006) how
to Integrate out all except the lowest ones (i.e.
r) of the tower and put the resulting Lagrangian
in HLS1 form

where the HLS parameters are given by hQCD
ones at a certain matching scale L ? Lc ? 4pfp .
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dualHLS1 Predicts

• Take this Lagrangian as a bare Lagrangian
  defined
• at L, do quantum loop calculations. Works as well
  as
• gHLS1 gauge theory of Harada and Yamawaki

Harada, Matsuzaki, Yamawaki 2006
But useless in medium!
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Strategy for Hot/Dense Matter
Question What does the infinite tower do in
hot/dense hadronic
matter? Answer We dont know! Guess from
gHLS1 of Harada and Yamawaki

• Match (a la Wilson) gHLS1 to QCD at L in the
• the background of temperature (T) and/or density
  (n).

Intrinsic T/n dependence
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One-loop RGE analysis
Harada, Kim, Sasaki, Yamawaki gt 2000

• One fixed point consistent with gQCD is the
• vector manifestation (VM) fixed point

• As (T, n) ? (TcSR, ncSR) in the chiral limit,

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Consequences

• Strong deviation from vector dominance in
• dilepton process in heavy ion collisions

pp-?r?ee- (mm-) suppressed in hot/dense
medium, should affect drastically the analysis
of NA60, CERES etc.

• Exotic doorway to color superconductivity

Half-skyrmion phase as non-normal Fermi liquid
(as In high T superconductivity) and deconfined
quantum critical phenomenon
Seminar March 10th

• Kaon condensation, compact stars etc.

Light-mass black holes and cosmological
natural selection scenario
Brown, Lee, R, arXiv0802.2997
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gHLS1 on Vector Dominance
EM-HLS coupling
g
p, N(skyrmion)
T0 n0
T?0 n?0
Form Factors

• Pion VD ? a2
  a? 1 VD

• Nucleon VD
  a lt 1 (?) VD
• a 1? avm

The Tower!!
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p form factor drastically is affected
Harada Sasaki 2006
T0
T 0.9 Tc
without
VD violation
with
Dileptons?
Old VD used by everybody else -- is totally
wrong!! And all the great theoretical stuff based
on old VD??
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Thanks