Hadronic matter from the vector manifestation (VM) fixed point Mannque Rho Chiral 05/RIKEN

Outline Physics around the VM fixed point Physics around the VM fixed point Question of scales Question of scales Need for, and power of, HLS (hidden local symmetry) for vector mesons Need for, and power of, HLS (hidden local symmetry) for vector mesons VD (vector dominance) is generically maximally violated in nature VD (vector dominance) is generically maximally violated in nature Predictions: (1) M *  near chiral restoration, (2)   Pentaquark, (3) “strange nugget” out of a neutron star Predictions: (1) M *  near chiral restoration, (2)   Pentaquark, (3) “strange nugget” out of a neutron star

HLS : two points where theory is precisely known VM VAC VM

Propose: Fluctuate around VM Instead of around VAC

Scales (hadrons) E << m  : E << m  : E ~ m  : E ~ m  : “Ultraviolet complete” to QCD Baryons must arise as skyrmions

Scales (nuclei) E << m   E << m   E  m   E  m   E  m   E  m   Tower of vector mesons figure.

Physics with or without vector mesons can be drastically different

Case: Pion velocity v  near T c Linear  model (with no vector mesons): Linear  model (with no vector mesons): v  = 0 ( Son and Stephanov 2002) v  = 0 ( Son and Stephanov 2002) Hidden local symmetry (with vector mesons) Hidden local symmetry (with vector mesons) v   1 ( Harada, Rho and Sasaki 2004) v   1 ( Harada, Rho and Sasaki 2004) Caveat: Lorentz symmetry breaking leads to a small deviation from the velocity of light

Vector mesons with or without local gauge invariance can lead to drastically different physics

Case: Vector meson mass at T c Without gauge invariance, with vector dominance (VD): Without gauge invariance, with vector dominance (VD): m   c )/ m   Pisarski 1998 m   c )/ m   Pisarski 1998 With hidden gauge invariance, hence VD maximally With hidden gauge invariance, hence VD maximally violated: violated: m   c )/ m   Harada, Yamawaki m   c )/ m   Harada, Yamawaki Harada, Sasaki 2002 Harada, Sasaki 2002 (Brown, Rho 1991) (Brown, Rho 1991)

Desperately looking for guidance No guidance from QCD gauge theory proper, so groping in the darkness gives the quagmire!!! But string theory AdS/QCD hidden local symmetry!

Why need local gauge symmetry for the vector mesons? Consider physics of the EFT given by  Massive Yang-Mills Lagrangian with mass m A =g 2 f valid at low energy: But there is no gauge invariance  If one wants to go to a higher energy scale, say, 4  f, then one is at a loss with no symmetry guidance: + many other terms “Quagmire” results I.e.

Solution Introduce Goldstone bosons U=exp (i  /f) and an additional gauge field A 1 Write gauge-invariant Lagrangian involving A 2, A 1 and U

Gauge fix : U =1 or  =0 Let g 1 =0, decoupling A 1 Gauge invariant Unitary gauge “Hidden gauge invariance” with the  field eaten up to give the mass to A 2 : Higgsing

What’s gained + “quagmire” Book-keeping order by order (e.g., ChPT) Valid to the scale 4  f beyond which “ultraviolet completed” to a fundamental theory No problem handling m A 0. Important for later!

Hidden Local Symmetry (HLS) a la Harada-Yamawaki Pick the matching scale:  M =  4  f   GeV Pick relevant degrees of freedom below  M :    SU( N f ), ignore scalars (can be put in if needed),  integrate out a 1, glueballs etc. Baryons emerge as skyrmions Pick relevant degrees of freedom above  M : quark, G  Ultraviolet complete by Wilsonian matching at  M Quantize at loop orders : RGE Harada and Yamawaki Phys. Rept. 381 (2003)

Identify with HY fields:  L † =  L,  R =  R Note: a=1  “Theory-space locality” HY Lagrangian “Open moose”

(De)Constructing 5 th Dimension Let  0, put nearest-neighbor vectors A  k connected by link fields  k Tower of vectors Generalize open moose 5-D gauge theory with 5 th -D on lattice!!

Let N ∞ and go to continuum Pure Yang-Mills + Chern-Simons in curved space in five-D To do QCD, put ultraviolet and infrared cutoffs in the fifth D Son and Stephanov 2004 Others … With

What’s the big deal? Tower of hidden local symmetry gives 5-D (YM) gauge theory String theory gives the same 5-D gauge theory which is dual to QCD on the 4-D surface !

Glashow explained that the Albert Einstein, who failed in his search to find a unified theory of forces in the universe, spent the last three decades of his life isolated from the scientific community. "It is tragic," Glashow said, "but now, we have the string theorists, thousands of them, that also dream of explaining all the features of nature. They just celebrated the 20th anniversary of superstring theory. "So when one person spends 30 years, it's a waste, but when thousands waste 20 years in modern day, they celebrate with champagne. I find that curious." Glashow on string theory

String theory HLS Maldacena 97: AdS/CFT duality Maldacena 97: AdS/CFT duality Karch, Katz, Witten, Klebanov, Strassler … : Deform geometry in the dual gravity sector, introduce quark flavor D branes as probes and construct gravity theory in the bulk (5D) dual to a gauge theory on the surface (4D) Karch, Katz, Witten, Klebanov, Strassler … : Deform geometry in the dual gravity sector, introduce quark flavor D branes as probes and construct gravity theory in the bulk (5D) dual to a gauge theory on the surface (4D) Sakai, Sugimoto 04: Succeeded to construct a bulk theory in 5-D dual to QCD on 4-D surface with correct chiral symmetry breaking. Sakai, Sugimoto 04: Succeeded to construct a bulk theory in 5-D dual to QCD on 4-D surface with correct chiral symmetry breaking.

Upshot 5-D YM theory in the bulk leads (via holography) to 4-D HLS of a tower of vector mesons: the parameters of the theory fixed by the bulk constants Confined to the lowest member of the tower, , it leads to HY theory!

Therefore HLS with  is “dual” to QCD Baryons must arise as skyrmions in HLS theory

Vector manifestation in the chiral limit C. Sasaki’s Talk  HLS matched to QCD at  M Flows to the “VM fixed point” g 0 f  0 a 1 (  0) As (T, n, N f ) (T c, n c, N f c )

The vector meson mass vanishes near the critical point m V ~ a 1/2 F  g ~ + … And a ~ 1. Quark mass corrections Consequence  V / m V ~ + … Falsifiable Prediction

Physics Around VM  HLS is well defined at the VM so if nature is not too far from the VM, why not start from there? HY showed that both g and f  depart from 0 but a stays ~ 1 (or  ~ 0), i.e., “theory-space local”.

Vector Dominance  L=-2eag F  2 A  Tr [   Q ] + 2i (1- a/2 ) A  Tr [ V  Q ]        a=2 : VD  a=1 : maximal violation of VD

Evidences that a~1 EM pion mass difference EM pion mass difference “Dynamical origin of Little Higgs” (Harada, Yamawaki 03) “Dynamical origin of Little Higgs” (Harada, Yamawaki 03) Chiral doubling of heavy-light hadrons Chiral doubling of heavy-light hadrons (Harada, Rho, Sasaki 04) (Harada, Rho, Sasaki 04) Nucleon form factors: Violation of VD Nucleon form factors: Violation of VD (Iachello, Jackson, Lande 73, Brown, Rho, Weise 86) (Iachello, Jackson, Lande 73, Brown, Rho, Weise 86) Matter in heat bath: Violation of VD Matter in heat bath: Violation of VD (Harada, Sasaki 04) (Harada, Sasaki 04)

Prediction 1 Parametric mass of all light-quark hadrons M scales in medium near VM as Parametric mass of all light-quark hadrons M scales in medium near VM as M * /M ≈ ( * / ) n +…+ O (m quark ) M * /M ≈ ( * / ) n +…+ O (m quark ) The  and  (parametric and pole) masses: The  and  (parametric and pole) masses: m   m   0 with the width going to zero more quickly. m   m   0 with the width going to zero more quickly. (Explicit  SB will smear the sharp predictions.) (Explicit  SB will smear the sharp predictions.) The D-meson chiral splitting will go to zero modulo The D-meson chiral splitting will go to zero modulo quark-mass corrections. quark-mass corrections. Etc. etc. Etc. etc.

Prediction 2 Since HLS is dual to QCD, baryons must come as skyrmions The celebrated DPP (rigid rotor) skyrmion is not consistent with large N c. The bound kaon-soliton skyrmion for S=±1 is consistent with large N c. without HLS But there is no bound S=+1   without HLS  Itzahki et al 2004 ). With HLS, Vector mesons are very (not) important for S>0 (<0) baryons. K + (K - ) binding is very sensitive (insensitive) to a (or  ) which acts as a “magnetic field” K + will be bound to s K + will be bound to skyrmion to produce   pentaquark

  - skyrmion complex Bound for a < 1.3 Unbound for a > 1.3  AdS/QCD gives “ a” ~ 1.3 HLS/VM gives a  ~ Large N c Therefore for large N c, K + is bound to skyrmion ~

Physics of bound    (Park, Rho, Min 04)

Prediction 3 Brown, Lee, Rho 05 Scoop a nugget containing 2 neutrons, 1 proton and 1 K - out of a neutron star on the way to a black hole with kaon condensed at n  3.1 n 0 (Thorsson, Prakash, Lattimer 94). Here on the average one electron is replaced by a K - Strange nugget of a neutron star S 0 (3115): nnpK - ? In progress Fluctuating around VM