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.

• Received 12 December 2012

DOI:https://doi.org/10.1103/PhysRevD.87.034513