Anti-Periodic Boundary Conditions in Supersymmetric DLCQ

TL;DR

This paper introduces a novel anti-periodic boundary condition formulation of supersymmetric discrete light-cone quantization (SDLCQ) that allows for the study of BPS states, though with slow convergence.

Contribution

It proposes a new anti-periodic boundary condition approach in SDLCQ that breaks supersymmetry at finite resolution but restores it in the continuum limit, enabling BPS state analysis.

Findings

Method breaks supersymmetry at finite resolution

Requires no renormalization

Converges slowly to the continuum limit

Abstract

It is of considerable importance to have a numerical method for solving supersymmetric theories that can support a non-zero central charge. The central charge in supersymmetric theories is in general a boundary integral and therefore vanishes when one uses periodic boundary conditions. One is therefore prevented from studying BPS states in the standard supersymmetric formulation of DLCQ (SDLCQ). We present a novel formulation of SDLCQ where the fields satisfy anti-periodic boundary conditions. The Hamiltonian is written as the anti-commutator of two charges, as in SDLCQ. The anti-periodic SDLCQ we consider breaks supersymmetry at finite resolution, but requires no renormalization and becomes supersymmetric in the continuum limit. In principle, this method could be used to study BPS states. However, we find its convergence to be disappointingly slow.