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Alex Kalloniatis (CSSM, Adelaide) & Sergei N. Nedelko (JINR, Dubna)

CHIRALITY IN A DOMAIN MODEL FOR THE QCD VACUUM. Alex Kalloniatis (CSSM, Adelaide) & Sergei N. Nedelko (JINR, Dubna). QCD@Work, Conversano, June 14-18, 2003. Singular Fields in the QCD Partition Function. In general, action will be infinite . exp(-action)=0.

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Alex Kalloniatis (CSSM, Adelaide) & Sergei N. Nedelko (JINR, Dubna)

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  1. CHIRALITY IN A DOMAIN MODEL FOR THE QCD VACUUM Alex Kalloniatis (CSSM, Adelaide) & Sergei N. Nedelko (JINR, Dubna) QCD@Work, Conversano, June 14-18, 2003.

  2. Singular Fields in the QCD Partition Function In general, action will be infinite. exp(-action)=0. no contribution from such singular fields. EXCEPTION: when fields satisfy specific conditions.

  3. Example: Abelian singular field in YM theory

  4. 4-dimensional Euclidean space fields in a given domain interact with fluctuations in rest of system replace with a mean field in each domain and treat effective domains as noninteracting On average, each domain has: • hyperspherical geometry • same radius • constant field strength • self-dual (SD) or anti-self-dual (ASD) • colour direction Abelian 2 Model parameters: average radius, R average field strength, B • domain positions • E&B field orientations • colour orientations in Abelian subgroup • random assignment of SD and ASD Collective coordinates (to be summed/integrated over in path-integral):

  5. Topological charge: absolute value of topological charge per domain Topological susceptibility: Area law in Wilson loop & string tension: C 2L for large L

  6. large (c.f. 0.01 GeV4) non-integer

  7. Dirac operator in a single domainKalloniatis & Nedelko, PRD 66 074020 (2002). In domain model: BC explicitly breaks chiral symmetry: UA(1)→ Z2

  8. Solution: angular momentum quantum numbers: k,m1,m2 colour projection spin-field projection

  9. discrete spectrum for each k: principal quantum #, n • spectrum asymmetric • similar behaviour for all k • NO ZERO MODES • spectrum in a single domain NOT the entire ensemble!

  10. Comparison with ``chirality’’ measurements on the lattice: Dirac eigenmodes as filters for gluonic structures in the ``vacuum’’. • To compare lattice results with domain model: • Mimic lattice spacing: smear over centre. • Do for each a. • Distribute a randomly through ensemble.

  11. Spectral Asymmetry and Zeta Function Regularisation of Fermion determinants Free energy and quark determinant for single domain: Trick for computing spectral sums:

  12. Representation of square Dirac operator

  13. QUARK CONDENSATE Zeta function with mass term h(1) breaks symmetry between minima of free energy:

  14. Domain Boundary Condition Infinitesimal mass term Thermodynamic Limit

  15. Domain model confines static quarks and provides for spontaneously broken chiral symmetry Kalloniatis, Nedelko: PRD 64, 114025 (2001), Kalloniatis, Nedelko: PRD 66, 074020 (2002).

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