Exact Flow Equations and the U(1)-Problem

Abstract

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.

22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev. D

References in corpus (5)

• Instantons in QCD
• Gauge Invariance, the Quantum Action Principle, and the Renormalization Group
• The Heavy Quark Potential from Wilson's Exact Renormalization Group
• Renormalization of the Topological Charge in Yang-Mills Theory
• The Ward Identity from the Background Field Dependence of the Effective Action

Cited by in corpus (32)

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• Chiral symmetry breaking in continuum QCD
• Infrared behaviour and fixed points in Landau gauge QCD
• Relevance of the axial anomaly at the finite-temperature chiral transition in QCD
• Universality of spontaneous chiral symmetry breaking in gauge theories
• Two flavor chiral phase transition from nonperturbative flow equations
• Quantum gravity: a fluctuating point of view
• Wilsonian flows and background fields
• The QCD Phase Boundary from Quark-Gluon Dynamics
• Renormalisation group flows for gauge theories in axial gauges
• Fluctuations and the axial anomaly with three quark flavors
• Chiral Susceptibility in (2+1)-flavour QCD
• Fierz-complete NJL model study III: Emergence from quark-gluon dynamics
• Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly
• Mass sensitivity of the three-flavor chiral phase transition
• Gravitational wave from dark sector with dark pion
• Fierz-complete NJL model study II: towards the fixed-point and phase structure of hot and dense two-flavor QCD
• Functional Renormalization Group Study of the Chiral Phase Transition Including Vector and Axial-vector Mesons
• Thermal properties and evolution of the $U_A(1)$ factor for 2+1 flavors
• Functional dependence of axial anomaly via mesonic fluctuations in the three flavor linear sigma model
• U(2)xU(2)-symmetric fixed point from the Functional Renormalization Group
• The Myriad Uses of Instantons
• Gravitational instantons and anomalous chiral symmetry breaking
• Pion and $\eta$-meson mass splitting at the two-flavour chiral crossover
• Do Instantons Like a Colorful Background?
• New Insight about the Effective Restoration of U_A(1) Symmetry
• Hubble selection of the weak scale from QCD quantum critical point
• The $\theta$-vacuum from functional renormalisation