From supermembrane to super Yang-Mills theory

TL;DR

This paper derives maximally supersymmetric Yang-Mills theories from wrapped supermembranes using matrix regularization, revealing T-duality relations without explicitly referencing D-branes or superstring dualities.

Contribution

It provides a novel derivation of super Yang-Mills theories from supermembranes that naturally encodes T-duality, independent of D-brane or superstring duality assumptions.

Findings

Yang-Mills theories derived from supermembranes via matrix regularization.

Fourier coefficients in supermembrane theory correspond to matrix elements.

Exact T-duality relations emerge from the supermembrane framework.

Abstract

We derive p+1-dimensional (p=1,2) maximally supersymmetric U(N) Yang-Mills theory from the wrapped supermembrane on $R^{11-p}\times T^{p}$ in the light-cone gauge by using the matrix regularization. The elements of the matrices in the super Yang-Mills theory are given by the Fourier coefficients in the supermembrane theory. Although our approach never refers to both D-branes and superstring dualities, we obtain the relations which exactly represent T-duality.