M Theory Extensions of T Duality

TL;DR

This paper explores two M theory extensions of T duality, showing how compactifications relate M theory to type IIB and SO(32) superstring theories with specific size relationships.

Contribution

It introduces two novel M theory generalizations of T duality, expanding the understanding of dualities in string theory.

Findings

M theory on a torus is dual to type IIB on a circle

M theory on a cylinder is dual to SO(32) superstring on a circle

Circle size relates to dual manifold area by -3/4 power

Abstract

T duality expresses the equivalence of a superstring theory compactified on a manifold K to another (possibly the same) superstring theory compactified on a dual manifold K'. The volumes of K and K' are inversely proportional. In this talk we consider two M theory generalizations of T duality: (i) M theory compactified on a torus is equivalent to type IIB superstring theory compactified on a circle and (ii) M theory compactified on a cylinder is equivalent to SO(32) superstring theory compactified on a circle. In both cases the size of the circle is proportional to the -3/4 power of the area of the dual manifold.