T Duality in M(atrix) Theory and S Duality in Field Theory

TL;DR

This paper explores how T duality in M(atrix) theory relates to S duality in field theories, revealing deep connections between different super Yang-Mills theories through compactification and dualities.

Contribution

It demonstrates the relationship between T duality in matrix models and S duality in field theories, especially highlighting the electric-magnetic duality in N=4 SYM.

Findings

T dualities require nontrivial identifications between SYM theories

In the case of K≥3, dualities relate different super Yang-Mills theories

The electric-magnetic duality in N=4 SYM emerges from T duality considerations

Abstract

The matrix model formulation of M theory can be generalized to compact transverse backgrounds such as tori. If the number of compact directions is K then the matrix model must be generalized to K+1 dimensional super Yang Mills theory on a compact space. If K is greater than or equal to 3, there are T dualities which which require highly nontrivial identifications between different SYM theories. In the simplest case we will see that the requirement reduces to the well known electric- magnetic duality of N=4 SYM theory in 3+1 dimensions.