SDLCQ: Supersymmetric Discrete Light Cone Quantization

TL;DR

This paper discusses SDLCQ, a method that preserves supersymmetry exactly in discrete light cone quantization, enabling detailed study of supersymmetric field theories across various dimensions.

Contribution

It introduces SDLCQ, a formulation of DLCQ that maintains supersymmetry exactly, and reviews its application to multiple supersymmetric theories.

Findings

SDLCQ preserves supersymmetry exactly in discretized models.

Application to 2D theories with various supersymmetries demonstrates its effectiveness.

Exploration of zero modes, vacuum structure, and higher-dimensional theories.

Abstract

In these lectures we discuss the application of discrete light cone quantization (DLCQ) to supersymmetric field theories. We will see that it is possible to formulate DLCQ so that supersymmetry is exactly preserved in the discrete approximation. We call this formulation of DLCQ, SDLCQ and it combines the power of DLCQ with all of the beauty of supersymmetry. In these lecture we will review the application of SDLCQ to several interesting supersymmetric theories. We will discuss two dimensional theories with (1,1), (2,2) and (8,8) supersymmetry, zero modes, vacuum degeneracy, massless states, mass gaps, theories in higher dimensions, and the Maldacena conjecture among other subjects.