Exact Results in Discretized Gauge Theories

TL;DR

This paper applies localization techniques to discretized supersymmetric gauge theories on Riemann surfaces, enabling exact calculations of partition functions and operator vevs that depend only on topological features.

Contribution

It introduces a method to exactly evaluate key quantities in discretized supersymmetric gauge theories, linking localization to lattice models and topological invariants.

Findings

Partition function depends only on Euler characteristic and area.

Vacuum expectation value of Q-closed operator is topologically invariant.

Method simplifies numerical analysis of supersymmetric lattice models.

Abstract

We apply the localization technique to topologically twisted N=(2,2) supersymmetric gauge theory on a discretized Riemann surface (the generalized Sugino model). We exactly evaluate the partition function and the vacuum expectation value (vev) of a specific Q-closed operator. We show that both the partition function and the vev of the operator depend only on the Euler characteristic and the area of the discretized Riemann surface and are independent of the detail of the discretization. This localization technique may not only simplify numerical analysis of the supersymmetric lattice models but also connect the well-defined equivariant localization to the empirical supersymmetric localization.