Generalized Instantons on Complex Projective Spaces

TL;DR

This paper explores generalized self-duality relations for gauge fields on complex projective spaces, constructing explicit solutions using higher-order field strengths and non-single trace terms, advancing understanding of gauge theories in complex geometries.

Contribution

It introduces a new class of pseudo-energies with higher-order field strengths and constructs explicit solutions to generalized self-duality equations on complex projective spaces.

Findings

Constructed explicit solutions of codimension 2n to generalized self-duality equations.

Extended the framework of gauge theories to include higher-order field strength terms.

Demonstrated the necessity of non-single trace terms for Bogomol'nyi completion on complex projective spaces.

Abstract

We study a class of generalized self-duality relations in gauge theories on the complex projective space with the Fubini-Study metric. Our theories consist of only gauge fields with gauge group U(n). The pseudo-energies which we consider contain higher orders of field strength and are labeled by an integer p smaller than or equal to [n/2]. For making the Bogomol'nyi completion we need non-single trace terms in the pseudo-energies, unlike the models defined on spheres, which were studied previously. We construct an explicit solution of codimension 2n to generalized self-duality equations as Bogomol'nyi equations, by using a part of the spin connection.