SUSY WT identity in a lattice formulation of 2D $\mathcal{N}=(2,2)$ SYM

TL;DR

This paper investigates the SUSY Ward-Takahashi identity in a lattice formulation of 2D $ abla=(2,2)$ SYM, demonstrating its continuum limit validity and justifying a Hamiltonian density prescription.

Contribution

It provides a perturbative proof that the SUSY WT identity is preserved in the continuum limit without operator renormalization and confirms the Hamiltonian density prescription within this framework.

Findings

SUSY WT identity is reproduced in the continuum limit without tuning.

The Hamiltonian density prescription is justified via operator algebra.

Explicit confirmation of the SUSY WT identity at first nontrivial order.

Abstract

We address some issues relating to a supersymmetric (SUSY) Ward-Takahashi (WT) identity in Sugino's lattice formulation of two-dimensional (2D) $\mathcal{N}=(2,2)$ $SU(k)$ supersymmetric Yang-Mills theory (SYM). A perturbative argument shows that the SUSY WT identity in the continuum theory is reproduced in the continuum limit without any operator renormalization/mixing and tuning of lattice parameters. As application of the lattice SUSY WT identity, we show that a prescription for the hamiltonian density in this lattice formulation, proposed by Kanamori, Sugino and Suzuki, is justified also from a perspective of an operator algebra among correctly-normalized supercurrents. We explicitly confirm the SUSY WT identity in the continuum limit to the first nontrivial order in a semi-perturbative expansion.