Topological defects in nonlocal field theories

TL;DR

This paper investigates topological defects, specifically domain walls, within nonlocal field theories containing infinite-order differential operators, revealing that nonlocality affects their width and energy, and establishing constraints on the nonlocality scale.

Contribution

It provides the first analysis of topological defects in nonlocal field theories, deriving approximate solutions and constraints on the nonlocality scale.

Findings

Nonlocality makes domain walls thinner.

Energy per unit area of domain walls decreases due to nonlocality.

A theoretical constraint on the nonlocality energy scale is established.

Abstract

In this paper, we study for the first time topological defects in the context of nonlocal field theories in which Lagrangians contain infinite-order differential operators. In particular, we analyze domain walls. Despite the complexity of non-linear infinite-order differential equations, we are able to find an approximate analytic solution. We first determine the asymptotic behavior of the nonlocal domain wall close to the vacua. Then, we find a linearized nonlocal solution by perturbing around the well-known local 'kink', and show that it is consistent with the asymptotic behavior. We develop a formalism to study the solution around the origin, and use it to verify the validity of the linearized solution. We find that nonlocality makes the width of the domain wall thinner, and the energy per unit area smaller as compared to the local case. For the specific domain wall solution under investigation, we derive a theoretical constraint on the energy scale of nonlocality which must be larger than the corresponding symmetry-breaking scale. We also briefly comment on other topological defects like string and monopole.