Fermionic instantons

TL;DR

This paper introduces a new class of non-perturbative fermionic solutions in Euclidean supergravity, called fermionic instantons, which are half-BPS, nonsingular, and have zero action, constructed using (anti)self-dual Yang-Mills fields and Killing spinors.

Contribution

It identifies and constructs fermionic instantons in supergravity, extending the ADHM method to generate all solutions on specific gravitational backgrounds.

Findings

Fermionic instantons are half-BPS and nonsingular.

These solutions have zero action and obey (anti)self-duality.

They depend on spacetime torsion and are related to the gravitino as a gauge field.

Abstract

We demonstrate the existence of a broad class of non-perturbative fermionic solutions to the Euclidean supergravity equations of motion, which are half-BPS and nonsingular, possess zero action, and obey an (anti)self-duality condition. These are identified as fermionic instantons associated to the status of the gravitino as the gauge field of local supersymmetry. By explicitly constructing these configurations from combinations of (anti)self-dual Yang-Mills gauge fields and Killing spinors, we may leverage the ADHM method and generalisations thereof to provide all possible solutions on certain gravitational backgrounds. As one may expect, these solutions generate and are in turn intrinsically dependent upon spacetime torsion.