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Fermionic instantons

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.