Nonselfdual solutions for gauge fields in Schwarzschild and deSitter backgrounds for dimension $d\geq 4$

TL;DR

This paper constructs simple nonselfdual gauge field solutions in Schwarzschild and deSitter backgrounds across various dimensions, analyzing their properties and providing explicit numerical results for specific cases.

Contribution

It introduces a new class of nonselfdual solutions in curved backgrounds for dimensions d ≥ 4, including real and complex solutions with finite energy and action.

Findings

Finite energy and action solutions in Schwarzschild and deSitter backgrounds

Explicit numerical values for dimensions 4, 6, 7, 8, 9, 10

Special case analysis for dimension 5

Abstract

A particularly simple class of nonselfdual solutions are obtained for gauge fields in Schwarzschild and deSitter backgrounds. For Lorentz signature these have finite energy and finite action for Euclidean signature. In each case one obtains either real or a pair of complex conjugate solutions. The actions are easily computed for any dimension d. Numerical values are given for d= 4,6,7,8,9,10. It is explained why d=5 is a very special case. Possible continuations and generalizations of the results obtained are indicated. A particular solution for AdS_4 background is presented in the Appendix.