Monads, Strings, and M Theory

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 $T^2$.

36 pages, TeX, harvmac, minor corrections with added reference

References in corpus (8)

• Matrix String Theory
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• Matrix Description of M-theory on $T^4$ and $T^5$
• Proposals on nonperturbative superstring interactions
• Heterotic M(atrix) Strings and Their Interactions
• Heterotic Matrix String Theory
• Heterotic Strings from Matrices
• M(atrix) Theory on T5/Z2 Orbifold and Five-Branes

Cited by in corpus (4)

• M theory as a matrix extension of Chern-Simons theory
• Topological Matrix Model
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Proposal of a topological M(atrix) theory