Issues in M(atrix) Theory Compactification

TL;DR

This paper examines the challenges of M(atrix) theory compactifications on curved spaces, highlighting issues with decoupling of string states and implications for reproducing supergravity results.

Contribution

It identifies fundamental issues in curved space compactifications and proposes potential higher derivative corrections to address these problems.

Findings

String states do not decouple in curved space compactifications.

Finite quantum systems struggle to reproduce supergravity results.

Higher derivative terms may be necessary for accurate modeling.

Abstract

We discuss issues concerning M(atrix) theory compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane $v^4$ amplitude, unlike the flat space case. This argument shows that a large class of quantum mechanical systems with a finite number of degrees of freedom cannot reproduce supergravity answers. We discuss the specific example of an ALE space and suggest sources of possible higher derivative terms that might help reproduce supergravity results.