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**Topological Structure of Dense Hadronic Matter**

May 2006 Trieste Topological Structure of Dense Hadronic Matter V. Vento Universitat de València Colaborators: Heejung Lee (APCTP), Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay)

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Introduction A theory for Nuclear Structure Dense Skyrmion Matter Pions in Dense Skyrmion Matter Sliding Vaccua Vector Mesons Ongoing work Concluding remarks

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1. Introduction

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**Relevant degrees of freedom?**

Theory Effective Relevant degrees of freedom? Dynamics?

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QCD Effective Theory Observation

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**Quantum Chromo-Dynamics**

Effective Theory at zero Temp./Density Effective Theory at finite Temp./Density

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**2. A theory for Nuclear Structure**

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Skyrme’s Old Idea 1960, T. H. R. Skyrme

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**U(x) : mapping from R3-{ }=S3 to SU(2)=S3**

Skyrme’s Old Idea 1960, T. H. R. Skyrme U(x) : mapping from R3-{ }=S3 to SU(2)=S3 8 topological soliton R ~ 1 f m M ~ 1.5 GeV BARYON 1983 Adkins,Nappi,Witten,….

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Two Skyrmions Product Ansatz 1984 Orsay group, VV,..

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Toroidal B=2 Skyrmion 1988, Braaten,Carson,…. Manton and collaborators

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**Multi-Skyrmion Systems**

(surface of constant baryon number density)

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**Quantization is progressing**

Manton (B=2), Carson (B=3), Walhout (B=4), Irwin (B=4 to 9), Krusch (general formalism!)

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**B.-Y. Park, D.-P. Min, M. Rho, V. Vento,**

3. Dense Skyrmion Matter B.-Y. Park, D.-P. Min, M. Rho, V. Vento,

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**Skyrmion Crystal x y z z o 1985, CC, I. Klebanov,**

1987, Half-Skyrmion BCC, A. S. Goldhaber & N. S. Manton 1989, FCC & Half-Skyrmion CC, L. Castillejo et al., M. Kugler et al. o z x y z 2LFCC

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E/B vs. LF

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<tr(U)> Chiral symmetry restoration in dense matter?

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**3. Pions in Dense Skyrmion Matter B. -Y. Park, H. -J. Lee, M. Rho, V**

3. Pions in Dense Skyrmion Matter B.-Y. Park, H.-J. Lee, M. Rho, V. Vento

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Skyrme Model(mp=0) \

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**p dynamics(r=0) \ + p-skyrmion matter interactions Skyrmion matter**

Pion fluctuations on top of the skyrmion matter + p-skyrmion matter interactions

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**Wavefunction renormalization constant Z-1**

p dynamics(r=0) \ Wavefunction renormalization constant Z-1

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**Chiral Symmetry Restoration**

nuclear matter density p-N sigma term pion properties in dense medium?

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**GellMann-Oakes-Renner Relation**

Chiral symmetry restoration

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**GellMann-Oakes-Renner Relation**

pion condensation?

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Pion effective mass Pseudogap phase?

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**Pion velocity in medium**

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**Pseudogap? p s fp U still remains on the Chiral Circle But <U>=0**

Chiral Symmetry Restoration U still remains on the Chiral Circle But <U>=0 Zarembo, hep-ph/

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Zarembo, hep-ph/

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**4. Sliding Vacuua B.-Y. Park, H.-J. Lee, M. Rho, V. Vento**

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**Skyrme Lagrangian Trace Anomaly of QCD Ellis & Lanik, PLB(1985)**

mc ~ 720 MeV, fc~240 MeV

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fc c V(c) Vacuum (r=0) U=1 c=fc

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Naive Estimate E/B=M2(L)C2+M4(L) +Mm(L) C3+V(C)

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E/B

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In-medium quantities

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5. Vector Mesons

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**Hidden Local Gauge Symmetry**

rho & omega vector mesons HLG dilaton Trace Anomaly + Vector Meson Dominance

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**pions, chi, rho and omega 2 KSRF relation : mV=afpg2**

Bando, Kugo, Yamawaki, Phys. Rep. (1988)

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E/B

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**<s> & <c> without Omega**

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**<s> & <c> with Omega**

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6. Ongoing work

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**Skyrmion from Instanton**

1989, M. F. Atiyah & N. S.Manton Introduce variables describing the single skyrmion dynamics Classical mechanics Statistical mechanics Quantum mechanics Q orientation size position

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**time component of SU(2) gauge potential for the instanton field of charge N**

time-ordering constant matrix to make U approach 1 at infinity constant rotation matrix

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E/B vs. LF

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7. Concluding remarks

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**The skyrmion role in dense matter**

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**1. Construct dense skyrmion matter**

2. Fluctuations on top of this skyrmion matter. Properties and Dynamics of hadrons in dense medium.

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**Skyrme model Universal theory of baryons and mesons**

Nuclei and meson fluctuations Nuclear matter and mesons in the medium …….. Nuclear physicists dream! Caveats: Still very primitive! Crystal structures which should be Fermi liquids Quantum effects! Approach to QCD

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