Light scalars in strongly-coupled extra-dimensional theories

TL;DR

This paper explores how light scalar particles can emerge naturally in strongly-coupled five-dimensional gauge theories with compactified extra dimensions, using lattice simulations to go beyond perturbation theory.

Contribution

It provides the first non-perturbative evidence that light scalars can arise from extra-dimensional theories without fine tuning, through lattice studies of SU(2) Yang-Mills in five dimensions.

Findings

Identification of a dimensionally reduced phase with a light scalar state

The scalar mass is independent of the cutoff and controlled by the extra dimension size

Light scalars can be generated without fine tuning in lattice models with extra dimensions

Abstract

The low-energy dynamics of five-dimensional Yang-Mills theories compactified on S^1 can be described by a four-dimensional gauge theory coupled to a scalar field in the adjoint representation of the gauge group. Perturbative calculations suggest that the mass of this elementary scalar field is protected against power divergences, and is controlled by the size of the extra dimension R. As a first step in the study of this phenomenon beyond perturbation theory, we investigate the phase diagram of a SU(2) Yang-Mills theory in five dimensions regularized on anisotropic lattices and we determine the ratios of the relevant physical scales. The lattice system shows a dimensionally reduced phase where the four-dimensional correlation length is much larger than the size of the extra dimension, but still smaller than the four-dimensional volume. In this region of the bare parameter space, at energies below 1/R, the non-perturbative spectrum contains a \emph{light} scalar state. This state has a mass that is independent of the cut-off, and a small overlap with glueball operators. Our results suggest that light scalar fields can be introduced in a lattice theory using compactified extra dimensions, rather than fine tuning the bare mass parameter.