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Topological Structure of Dense Hadronic Matter: Theories and Implications

This work discusses the topological structure of dense hadronic matter, introducing a theoretical framework based on Skyrmion matter and pion dynamics. It highlights the historical context of Skyrme's ideas and their evolution in the study of nuclear structure, focusing on dense Skyrmion configurations, vector meson dominance, and the implications of chiral symmetry restoration in dense nuclear matter. The ongoing efforts in expanding the Skyrmion model through quantization and statistical mechanics are also explored, along with critical insights into sliding vacua and effective theories of Quantum Chromo-Dynamics (QCD).

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Topological Structure of Dense Hadronic Matter: Theories and Implications

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  1. May 2006 Trieste Topological StructureofDense 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)

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

  3. 1. Introduction

  4. Relevant degrees of freedom? Effective Theory Dynamics?

  5. QCD Effective Theory Observation

  6. QuantumChromo-Dynamics Effective Theory atzero Temp./Density Effective Theory at finite Temp./Density

  7. 2. A theory for Nuclear Structure

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

  9. Skyrme’s Old Idea topological soliton U(x) : mapping fromR3-{ }=S3toSU(2)=S3 8 R ~ 1 f m M ~ 1.5 GeV 1960, T. H. R. Skyrme BARYON 1983 Adkins,Nappi,Witten,….

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

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

  12. Multi-Skyrmion Systems (surface of constant baryon number density)

  13. Quantization is progressing Manton (B=2), Carson (B=3), Walhout (B=4), Irwin (B=4 to 9), Krusch (general formalism!)

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

  15. Skyrmion Crystal y y o o o o o o o o z z x x 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. z 2LFCC

  16. E/B vs. LF

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

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

  19. Skyrme Model(mp=0) \

  20. pdynamics(r=0) Skyrmion matter Pion fluctuations on top of the skyrmion matter \ + p-skyrmion matter interactions

  21. pdynamics(r=0) \ Wavefunction renormalization constant Z-1

  22. Chiral Symmetry Restoration p-Nsigma term nuclear matter density pion properties in dense medium?

  23. Chiral symmetry restoration GellMann-Oakes-Renner Relation

  24. pion condensation? GellMann-Oakes-Renner Relation

  25. Pseudogap phase? Pion effective mass

  26. Pion velocity in medium

  27. Pseudogap? Chiral Symmetry Restoration p fp s U still remains on the Chiral Circle But <U>=0 Zarembo, hep-ph/0104305

  28. Zarembo, hep-ph/0104305

  29. 4. Sliding VacuuaB.-Y. Park, H.-J. Lee, M. Rho, V. Vento

  30. Skyrme Lagrangian Trace Anomaly of QCD Ellis & Lanik, PLB(1985) mc ~ 720 MeV, fc~240 MeV

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

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

  33. E/B

  34. In-medium quantities

  35. 5. Vector Mesons

  36. Hidden Local Gauge Symmetry HLG Trace Anomaly rho & omega vector mesons dilaton + Vector Meson Dominance

  37. pions, chi, rho and omega KSRF relation : mV=afpg2 2 2 Bando, Kugo, Yamawaki, Phys. Rep. (1988)

  38. E/B

  39. <s> & <c> without Omega

  40. <s> & <c> with Omega

  41. 6. Ongoing work

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

  43. 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

  44. E/B vs. LF

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