Invariant formulation of the Functional Renormalisation Group method for $U(n)\times U(n)$ symmetric matrix models

Abstract

The Local Potential Approximation (LPA) to the Wetterich-equation is formulated explicitly in terms of operators, which are invariant under the $U(n)\times U(n)$ symmetry group. Complete formulas are presented for the two-flavor ($U(2)\times U(2)$) case. The same approach leads to a unique natural truncation of the functional driving the renormalisation flow of the potential of the three-flavor case ($U(3)\times U(3)$). The procedure applied to the $SU(3)\times SU(3)$ symmetric theory, results in an equation, which potentially allows an RG-investigation of the effect of the 't Hooft term representing the $U_A(1)$ anomaly, disentangled from the other operators.

to appear in Mod. Phys. Lett. A

References in corpus (14)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Optimised Renormalisation Group Flows
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Lectures on the functional renormalization group method
• The Phase Diagram of the Quark-Meson Model
• Chiral Symmetry Restoration at Nonzero Temperature in the SU(3) \times SU(3) Linear Sigma Model
• Renormalization Group Flow Equations and the Phase Transition in O(N)-models
• Equation of state and coarse grained free energy for matrix models
• The Functional Renormalization Group and O(4) scaling
• Second-order and Fluctuation-induced First-order Phase Transitions with Functional Renormalization Group Equations
• Functional renormalization group at finite density and Bose condensation
• Functional Renormalization for Chiral and U_A(1) Symmetries at Finite Temperature
• Finite temperature symmetry restoration in the U_L(3)xU_R(3) linear sigma model from a large-n approximation
• Spontaneously broken ground states of the U(n)_L x U(n)_R linear sigma model at large n

Cited by in corpus (10)

• Lectures on renormalization and asymptotic safety
• Fluctuation-induced modifications of the phase structure in (2+1)-flavor QCD
• Fluctuations and the axial anomaly with three quark flavors
• Functional renormalization group study of the two-flavor linear sigma model in the presence of the axial anomaly
• Functional Renormalization Group Study of the Chiral Phase Transition Including Vector and Axial-vector Mesons
• U(2)xU(2)-symmetric fixed point from the Functional Renormalization Group
• Fluctuation induced first order phase transition in U(n)xU(n) models using chiral invariant expansion of functional renormalization group flows
• Flowing in discrete gravity models and Ward identities: A review
• Chiral symmetry breaking patterns in the U_L(n)xU_R(n) meson model
• Field dependence of the Yukawa coupling in the three flavor quark-meson model