The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach

Abstract

We study the supersymmetric N=(2,2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called FlowPy. For weak couplings the quantum corrections to the bare mass found in lattice simulations is reproduced with high accuracy. But in the regime with intermediate couplings higher-order-operators that are not constrained by the nonrenormalization theorem yield the dominating contribution to the renormalized mass.

12 pages, 4 figures, version published by PRD

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• Asymptotic states and renormalization in Lorentz-violating quantum field theory
• Solving functional flow equations with pseudo-spectral methods
• Global Wilson-Fisher fixed points
• Critical $O(N)$ models in the complex field plane
• Critical behavior of supersymmetric O(N) models in the large-N limit
• Phases of supersymmetric O(N) theories
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• FlowPy - a numerical solver for functional renormalization group equations
• Numerical simulation of the $\mathcal{N}=(2,2)$ Landau-Ginzburg model
• Non-perturbative SQED beta function using functional renormalization group approach and the NSVZ exact beta function