Partial Supergravity Breaking and the Effective Action of Consistent Truncations

TL;DR

This paper investigates the properties of vacua in five-dimensional N=4 gauged supergravity, focusing on configurations with two broken supersymmetries, and examines one-loop corrections to the effective action in various string theory compactifications.

Contribution

It provides a detailed analysis of one-loop corrections to Chern-Simons terms in supergravity truncations, establishing conditions for consistent effective theories from string compactifications.

Findings

One-loop corrections to Chern-Simons terms vanish for Calabi-Yau threefolds with zero Euler number.

In squashed Sasaki-Einstein manifolds, gauge Chern-Simons terms cancel out, but gravitational terms remain non-zero.

Conditions for consistent truncations are derived from one-loop correction analyses.

Abstract

We study vacua of N = 4 half-maximal gauged supergravity in five dimensions and determine crucial properties of the effective theory around the vacuum. The main focus is on configurations with exactly two broken supersymmetries, since they frequently appear in consistent truncations of string theory and supergravity. Evaluating one-loop corrections to the Chern-Simons terms we find necessary conditions to ensure that a consistent truncation also gives rise to a proper effective action of an underlying more fundamental theory. To obtain concrete examples, we determine the N=4 action of M-theory on six-dimensional SU(2)-structure manifolds with background fluxes. Calabi-Yau threefolds with vanishing Euler number are examples of SU(2)-structure manifolds that yield N=2 Minkowski vacua. We find that that one-loop corrections to the Chern-Simons terms vanish trivially and thus do not impose constraints on identifying effective theories. This result is traced back to the absence of isometries on these geometries. Examples with isometries arise from type IIB supergravity on squashed Sasaki-Einstein manifolds. In this case the one-loop gauge Chern-Simons terms vanish due to non-trivial cancellations, while the one-loop gravitational Chern-Simons terms are non-zero.