Supersymmetric counterterms from new minimal supergravity

TL;DR

This paper classifies supersymmetric counterterms in four-dimensional theories on curved space, showing that preserving two supercharges eliminates ambiguities in the partition function, while one supercharge allows certain ambiguities.

Contribution

It provides a systematic classification of counterterms from new minimal supergravity and analyzes their impact on the supersymmetric partition function.

Findings

Counterterms vanish when two supercharges are preserved.

Partition function ambiguities depend on the number of preserved supercharges.

The classification aids in understanding supersymmetric theories on curved backgrounds.

Abstract

We present a systematic classification of counterterms of four-dimensional supersymmetric field theories on curved space, obtained as the rigid limit of new minimal supergravity. These are supergravity invariants constructed using the field theory background fields. We demonstrate that if the background preserves two supercharges of opposite chirality, then all dimensionless counterterms vanish, implying that in this case the supersymmetric partition function is free of ambiguities. When only one Euclidean supercharge is preserved, we describe the ambiguities that appear in the partition function, in particular in the dependence on marginal couplings.