The Moduli Space and M(atrix) Theory of 9d N=1 Backgrounds of M/String Theory

TL;DR

This paper explores the moduli space of nine-dimensional N=1 supersymmetric backgrounds in M and string theory, revealing new structures, limits, and a matrix theory formulation for various compactifications including Klein bottle and Mobius strip cases.

Contribution

It provides a detailed analysis of the moduli space, introduces a non-perturbative description of certain orientifold limits, and constructs the M(atrix) theory for these backgrounds.

Findings

Identification of two disconnected components in the rank 2 moduli space

Non-perturbative splitting of orientifold planes into D8-branes and charge (-1) planes

Construction of a 2+1D gauge theory M(atrix) model for M theory on a Klein bottle

Abstract

We discuss the moduli space of nine dimensional N=1 supersymmetric compactifications of M theory / string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a Mobius strip, the Dabholkar-Park background, CHL strings and asymmetric orbifolds of type II strings on a circle) fit together, and what are the weakly coupled descriptions in different regions of the moduli space. We argue that there are two disconnected components in the moduli space of theories with rank 2. We analyze in detail the limits of the M theory compactifications on a Klein bottle and on a Mobius strip which naively give type IIA string theory with an uncharged orientifold 8-plane carrying discrete RR flux. In order to consistently describe these limits we conjecture that this orientifold non-perturbatively splits into a D8-brane and an orientifold plane of charge (-1) which sits at infinite coupling. We construct the M(atrix) theory for M theory on a Klein bottle (and the theories related to it), which is given by a 2+1 dimensional gauge theory with a varying gauge coupling compactified on a cylinder with specific boundary conditions. We also clarify the construction of the M(atrix) theory for backgrounds of rank 18, including the heterotic string on a circle.