Cosmic string interactions induced by gauge and scalar fields

TL;DR

The paper investigates one-loop interactions between parallel cosmic strings induced by gauge and scalar fields in conical spacetimes. It shows that, to first order in deficit angles, a 4D gauge field is equivalent to a set of non-minimally coupled scalars with a specific coupling $\xi$, and confirms this by calculating the two-string interaction energy for both cases. The scalar result yields a closed-form interaction energy depending on the non-minimal couplings, and the gauge-field calculation reproduces this with $\xi = 1/2$, highlighting the role of contact terms and linking to black hole entropy renormalization. The findings provide a concrete holographic-like relation between gauge and scalar descriptions in curved backgrounds and illuminate the physical relevance of contact interactions beyond black hole entropy contexts.

Abstract

We study the interaction between two parallel cosmic strings induced by gauge fields and by scalar fields with non-minimal couplings to curvature. For small deficit angles the gauge field behaves like a collection of non-minimal scalars with a specific value for the non-minimal coupling. We check this equivalence by computing the interaction energy between strings at first order in the deficit angles. This result provides another physical context for the "contact terms" which play an important role in the renormalization of black hole entropy due to a spin-1 field.

Figures (1)

• Figure 1: Two parallel cosmic strings, separated by a distance $b$.