Monads, strings, and M theory

Abstract

The recent developmen ts in string theory suggest that the space-time coordinates should be generalized to non-comm uting matrices. P ostulating this suggestion as the fun- damen tal geometrical principle, w e form ulate a candidate for covariant second quantized RNS superstrings as a topological field theory in t wo dimensions. Our construction is a natural non-Abelian extension of the RNS string. It also naturally leads to a model with manifest 11-dimensional co variance, which we conjecture to be a form ulation of M theory . The non-comm uting space-time coordinates of the strings are further generalized to non- comm uting anti-symmetric tensors. The usual space-time picture and the free superstrings appear only in certain special phases of the model. W e 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 .