Supersymmetry-breaking compactifications on Riemann-flat manifolds

TL;DR

This paper investigates supersymmetry-breaking compactifications on Riemann-flat manifolds, analyzing the spectrum, effective potential, and relations to string theory mechanisms, providing new universal mass relations and explicit potential calculations.

Contribution

It introduces universal supertrace mass relations at each KK level and derives an explicit finite expression for the one-loop effective potential in supersymmetry-breaking compactifications.

Findings

The one-loop potential $V_1$ is negative definite and scales with inverse radii.

KK spectrum organizes into multiplets of broken supersymmetry.

Derived universal supertrace mass relations valid at each KK level.

Abstract

We consider compactifications of higher-dimensional supergravities on Riemann-flat manifolds of dimension d ($3 \le d \le 7$) that fully break supersymmetry at the classical level on a resulting D-dimensional Minkowski space. We systematically discuss consistency conditions, the Kaluza-Klein (KK) spectrum and harmonics, and the resulting one-loop effective potential $V_1$, focusing for illustration on maximal supergravity and d=3, in particular on the $T^3/Z_3$ and on the Hantzsche-Wendt manifolds. We show how the KK spectrum is organized in multiplets of the broken supersymmetry, derive new universal supertrace mass relations valid at each KK level and obtain an analytic finite expression for $V_1$ after resumming the contributions of all KK levels. In all examples $V_1$ is negative definite and scales with inverse powers of some internal radii. We extensively comment, when applicable, on the relation with the Scherk-Schwarz mechanism and with supersymmetry-breaking string compactifications on freely acting symmetric orbifolds. We also finally clarify the assumptions and constraints for Scherk-Schwarz reductions to correspond to twisted tori compactifications.