Absence of chiral symmetry breaking in multi-flavor strongly coupled lattice gauge theories

Abstract

We consider lattice gauge theories at strong coupling with gauge group $U({N}_{C})$, or $SU({N}_{C})$ restricted to the meson sector, and coupled to ${N}_{F}$ flavors of fundamental representation staggered fermions. We study the formation of a chiral condensate by means of resummation of a hopping expansion. Different classes of graphs become dominant as the parameter (${N}_{F}/{N}_{C}$) is varied. By performing graph resummation we obtain an equation for determining the condensate as a function of (${N}_{F}/{N}_{C}$) and mass $m$. For values of (${N}_{F}/{N}_{C}$) below a critical value, one reproduces the well-known result of the existence of a nonvanishing condensate solution in the $m=0$ limit. Above the critical (${N}_{F}/{N}_{C}$) value, however, no such solution exists, its abrupt disappearance indicating a first-order transition to a chirally symmetric phase with composite (colorless) excitation spectrum.