M Theory and P-Branes

TL;DR

This paper explores the classification of p-branes in compactified string theories and M theory, revealing their representations and bound states in eight dimensions, advancing understanding of brane dynamics and dualities.

Contribution

It introduces a classification scheme for p-branes based on SL(3,Z) and SL(2,Z) representations, connecting compactified string theories with M theory branes and bound states.

Findings

Branes classified by SL(3,Z) x SL(2,Z) representations.

Branes obtained via compactification of M theory on three torus.

Evidence for bound states of branes in eight dimensions.

Abstract

Ten dimensional type IIA and IIB theories with p-branes are compactified to 8-dimensions. It is shown that resulting branes can be classified according to the representations of $\bf {SL(3,Z) \times SL(2,Z)}$. These p-branes can also be obtained by compactification of M theory on three torus and various wrappings of membrane and five brane of the eleven dimensional theory. It is argued that there is evidence for bound states of the branes in eight dimensions as is the case in the interpretation of $\bf {SL(2,Z)}$ family of string solutions obtained by Schwarz.