On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory

Abstract

We study a discretization of $\mathcal{N}=2$ super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of {\it twisted} fields. In this paper we derive the action of the other twisted supersymmetries on the component fields and study, using Monte Carlo simulation, a series of corresponding Ward identities. Our results for SU(2) and SU(3) support a restoration of these additional supersymmetries without fine tuning in the infinite volume continuum limit. Additionally we present evidence supporting a restoration of (twisted) rotational invariance in the same limit. Finally we have examined the distribution of scalar field eigenvalues and find evidence for power law tails extending out to large eigenvalue. We argue that these tails indicate that the classical moduli space does not survive in the quantum theory.

35 pages, 14 figures, 18 tables. Results section rewritten to include discussion of phase quenching, continuum scaling and thermal boundary conditions. Version to be published in JHEP

References in corpus (4)

• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• Deconstruction and other approaches to supersymmetric lattice field theories
• Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with Exact Supersymmetry
• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions

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