Classical and Quantum Instantons in Yang-Mills Theory in the Background of de Sitter Spacetime

TL;DR

This paper explores classical and quantum instantons in Yang-Mills theory within de Sitter spacetime, providing explicit solutions, topological evaluations, fermion zero modes, and quantisation effects that enhance tunnelling amplitudes.

Contribution

It presents the first explicit instanton solutions in de Sitter background, verifies index theorems, constructs fermion zero modes, and quantifies quantum corrections to tunnelling amplitudes.

Findings

Explicit instanton solutions in de Sitter spacetime.

Quantitative evaluation of tunnelling amplitudes.

Quantum corrections enhance inter-vacua tunnelling.

Abstract

Instantons and their quantisation in pure Yang-Mills theory formulated in the background of de Sitter spacetime represented by spatially-closed ($k = 1$) Friedmann-Robertson-Walker metric are discussed. As for the classical treatment of the instanton physics, first, explicit instanton solutions are found and next, quantities like Pontryagin index and the semiclassical approximation to the inter-vacua tunnelling amplitude are evaluated. The Atiyah-Patodi-Singer index theorem is checked as well by constructing explicitly the normalizable fermion zero modes in this de Sitter spacetime instanton background. Finally, following the kink quantisation scheme originally proposed by Dashen, Hasslacher and Neveu, the quantisation of our instanton is performed. Of particular interest is the estimate of the lowest quantum correction to the inter-vacua tunnelling amplitude arising from the quantisation of the instanton. It turns out that the inter-vacua tunnelling amplitude gets enhanced upon quantising the instanton.