Isolated Critical Points for Scherk-Schwarz Compactifications of M-theory

TL;DR

This paper investigates Scherk-Schwarz compactifications of M-theory, identifying isolated critical points in the moduli space and proposing a duality covariant anomaly cancellation condition for orbifolded compactifications.

Contribution

It finds isolated critical points in M-theory compactifications and introduces a generalized anomaly cancellation condition for orbifolded models.

Findings

Identified unbroken duality groups and fixed points in moduli space.

Constructed explicit examples in various dimensions (d=8,6,5,4).

Proposed a duality covariant anomaly cancellation condition.

Abstract

We consider Scherk-Schwarz compactifications of M-theory (toroidal compactifications with a non-trivial spin structure) in various dimensions and find isolated critical points of the potential on the moduli space. We demonstrate this by identifying the unbroken duality group and finding isolated points on the moduli spaces which are fixed by elements of the unbroken duality group. We work out concrete examples involving compactifications down to $d=8,6, 5$ and $4$ spacetime dimensions. We also conjecture a duality covariant anomaly cancellation condition for M-theory on $T^n$ orbifolded by discrete $\mathbb Z_N$ symmetries acting as phases on the charge lattice. This anomaly cancellation condition generalizes the level matching requirement for perturbative string orbifolds.