Gravitational catalysis of merons in Einstein-Yang-Mills theory

TL;DR

This paper constructs regular Einstein-Yang-Mills solutions with meron gauge fields across various dimensions, demonstrating how gravity regularizes otherwise singular configurations, a phenomenon termed gravitational catalysis of merons.

Contribution

The study introduces new regular meron solutions in Einstein-Yang-Mills theory across multiple dimensions, highlighting the role of gravity in regularizing singular gauge configurations.

Findings

Meron solutions are regularized by gravity in various dimensions.

In 4D, the gravitating meron forms a Euclidean wormhole connecting different vacua.

In higher dimensions, merons are constructed via warped products of spheres and Einstein manifolds.

Abstract

We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter $\lambda$ determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing $\lambda$ to be different from its usual value of $1/2$. In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named "gravitational catalysis of merons".