Limits of Matrix Theory in Curved Space

TL;DR

This paper investigates the constraints on matrix string theory in curved spaces, showing it is only consistent on Ricci flat manifolds with zero six-dimensional Euler density, thus revealing fundamental limitations.

Contribution

It introduces a matrix sigma model approach to curved space matrix string theory and derives specific geometric conditions for its consistency.

Findings

Model only consistent on Ricci flat manifolds

Requires vanishing six-dimensional Euler density

Reduces to a matrix generalization of string beta function

Abstract

We study curved space versions of matrix string theory taking as a definition of the theory a gauged matrix sigma model. By analyzing the divergent terms in the loop expansion for the effective action we reduce the problem to a simple matrix generalization of the standard string theory beta function calculation. It is then demonstrated that the model can only be consistent for Ricci flat manifolds with vanishing six-dimensional Euler density.