Numerical Analysis of Discretized ${\cal N}=(2,2)$ SYM on Polyhedra

Abstract

We perform a numerical simulation of the two-dimensional ${\cal N}=(2,2)$ supersymmetric Yang-Mills (SYM) theory on the discretized curved space. The $U(1)_{A}$ anomaly of the continuum theory is maintained also in the discretized theory as an unbalance of the number of the fermions. In the process, we propose a new phase-quenched approximation, which we call the "anomaly-phase-quenched (APQ) method", to make the partition function and observables well-defined by $U(1)_{A}$ phase cancellation. By adopting APQ method, we estimate the Ward-Takahashi identity for exact SUSY on lattice and clarify contribution of the pseudo zero-modes to the pfaffian phase.

7 pages, 3 figures, 1 table, Proceedings of the 34th International Symposium on Lattice Field Theory (Lattice 2016), 24-30 July 2016, University of Southampton, UK