Renormalizing DLCQ Using Supersymmetry

TL;DR

This paper develops a supersymmetry-preserving renormalized Hamiltonian within the DLCQ framework, enabling non-perturbative analysis of supersymmetric gauge theories and improving convergence and singularity handling.

Contribution

It introduces a standard Hamiltonian formulation that yields finite, supersymmetric results at all DLCQ orders, automatically handles singularities, and preserves supersymmetry through irrelevant operators.

Findings

Exact reproduction of large N SDLCQ results

Automatic t'Hooft prescription for singularities

Enhanced convergence due to irrelevant operators

Abstract

Recent string theory developments suggest the necessity to understand supersymmetric gauge theories non-perturbatively, in various dimensions. In this work we show that there is a standard Hamiltonian formulation that generates a finite and supersymmetric result at every order of the DLCQ approximation scheme. We present this DLCQ renormalized Hamiltonian and solve for the bound states and the wave functions to verify that it exactly reproduces the large N SDLCQ results. We find that it has two novel features: it automatically chooses the t'Hooft prescription for renormalizing the singularities and it introduces irrelevant operators that serve to preserve the supersymmetry and improve the convergence. This is a first step in extending the advantages of SDLCQ to non-supersymmetric theories.