Self duality in unconventional conformal supersymmetry

TL;DR

This paper investigates (anti-)self duality conditions in an unconventional conformal supersymmetry framework, revealing bosonic solutions that generalize known gravitational instantons with torsion, and demonstrating their BPS saturation.

Contribution

It introduces a novel analysis of self-duality in conformal supersymmetry, constructing solutions with torsion that extend classical gravitational instantons.

Findings

Found bosonic solutions as gravitational instantons with torsion.

These solutions are (anti-)self-dual under a generalized dual operator.

Solutions saturate a BPS bound, indicating stability.

Abstract

In this work, we study (anti-)self duality conditions in unconventional conformal supersymmetry. We focus on a theory constructed in a Townsend-MacDowell-Mansouri form for an $SU(2,2|N)$ gauge connection with matter fields in the adjoint representation. We found bosonic solutions that correspond to analytic gravitational instantons with nontrivial torsion. These configurations can be regarded as the torsional generalization of the Taub-NUT/Bolt-AdS and Eguchi-Hanson metric and they are (anti-)self-dual with respect to a generalized dual operator. We explore their global properties and show that they saturate a BPS bound.