Higgs Mechanism in Nonlocal Field Theories

TL;DR

This paper investigates how nonlocal modifications to field theories affect the Higgs mechanism and gauge symmetry breaking, highlighting potential issues with ghost modes and proposing higher-dimensional symmetries as a solution.

Contribution

It analyzes the Higgs mechanism within nonlocal field theories inspired by string field theory, revealing potential ghost modes and suggesting higher-dimensional gauge symmetries as a remedy.

Findings

Nonlocal theories may include ghost modes near the nonlocal scale.

Such ghost modes pose challenges for UV completeness.

Higher-dimensional gauge symmetries could address these issues.

Abstract

We study spontaneous gauge symmetry breaking and the Higgs mechanism in nonlocal field theories. Motivated by the level truncated action of string field theory, we consider a class of nonlocal field theories with an exponential factor of the d'Alembertian attached to the kinetic and mass terms. Modifications of this kind are known to make mild the UV behavior of loop diagrams and thus have been studied not only in the context of string theory but also as an alternative approach to quantum gravity. In this paper we argue that such a nonlocal theory potentially includes a ghost mode near the nonlocal scale in the particle spectrum of the symmetry broken phase. This is in sharp contrast to local field theories and would be an obstruction to making a simple nonlocal model a UV complete theory. We then discuss a possible way out by studying nonlocal theories with extra symmetries such as gauge symmetries in higher spacetime dimensions.