Translational Symmetry Breaking in Higgs & Gauge Theory, and the Cosmological Constant

TL;DR

This paper explores how higher dimension operators in scalar gauge theories can break translational symmetry, potentially leading to crystal-like phases, and discusses implications for cosmological constant models and Lorentz violation constraints.

Contribution

It introduces a mechanism for translational symmetry breaking via higher dimension operators and models this holographically, linking it to cosmological constant phenomena.

Findings

Higher dimension operators can destabilize translationally invariant vacua.

Holographic models show RG running effects on symmetry breaking.

Phenomenological constraints challenge the realization of such phases in observable sectors.

Abstract

We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff, include terms that favour the breaking of translation (Lorentz) invariance, potentially resulting in striped, chequered board or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as $\bar{q} q$ and $\bar{q} F^{(2n)} q$. Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes RG running. A key phenomenological motive to look at such states is recent work that shows that the non-linear response in $R^2$ gravity to such short range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.