Fermion condensates and Lorentz symmetry breaking in strongly-coupled large N gauge theories

TL;DR

This paper investigates the spontaneous breaking of Lorentz symmetry in strongly-coupled large N lattice gauge theories through fermion condensate formation, revealing new condensates and symmetry locking phenomena.

Contribution

It demonstrates the existence of Lorentz symmetry breaking condensates and symmetry locking in large N lattice gauge theories, extending previous results on chiral symmetry breaking.

Findings

Existence of fermion condensates that break Lorentz symmetry.

Formation of condensates that lock internal and Lorentz symmetries.

Recovery of known chiral symmetry breaking results.

Abstract

The possibility of Lorentz symmetry breaking (LSB) has attracted considerable attention in recent years. Spontaneous LSB, in particular, offers the attractive prospect of the graviton as a Nambu-Golstone boson. Here we consider the question of spontaneous LSB in lattice gauge theories via formation of fermion condensates in the strong coupling and large N limits. We employ naive massless fermions in a fermionic hopping expansion in the presence of sources coupled to various condensate operators of interest. The expansion is summed in the large N limit in two equivalent ways: (i) direct summation of all leading N graphs; and (ii) construction of the corresponding large N effective action for composite operators. When sources are turned off a variety of fermionic condensates is found to persist. These include the chiral symmetry breaking condensates, thus recovering previous results, but also some LSB condensates, in particular, axial vector and rank-2 tensor condensates. Furthermore, in the presence of internal (global) symmetry groups, formation of condensates "locking" internal and external (Lorentz subgroup) symmetries is found to also become possible. Some implications and open questions are briefly discussed.