1105.3720 (E. T. Tomboulis)

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

E. T. Tomboulis

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.

View original: http://arxiv.org/abs/1105.3720