Monads, Strings, and M Theory

TL;DR

This paper proposes a covariant, non-Abelian extension of superstring theory using non-commuting matrices, aiming to formulate a candidate for M theory with 11-dimensional covariance and novel algebraic structures.

Contribution

It introduces a topological field theory framework for superstrings with non-commuting coordinates, extending the RNS string and conjecturing a formulation of M theory.

Findings

Derived algebraic equations for the model's moduli space

Constructed a non-Abelian, covariant superstring model

Tested aspects of the conjectured M theory on T^2 compactification

Abstract

The recent developments in string theory suggest that the space-time coordinates should be generalized to non-commuting matrices. Postulating this suggestion as the fundamental geometrical principle, we formulate a candidate for covariant second quantized RNS superstrings as a topological field theory in two dimensions. Our construction is a natural non-Abelian extension of the RNS string. It also naturally leads to a model with manifest 11-dimensional covariance, which we conjecture to be a formulation of M theory. The non-commuting space-time coordinates of the strings are further generalized to non-commuting anti-symmetric tensors. The usual space-time picture and the free superstrings appear only in certain special phases of the model. We derive a simple set of algebraic equations, which determine the moduli space of our model. We test some aspects of our conjectual M theory for the case of compactification on $T^2$.