Convergent expansions for excited glueball masses in 2+1 strongly coupled lattice gauge theories

Abstract

It is known that the mass spectrum of a strongly coupled (β=2/g2 small) 2+1 Wilson action lattice gauge theory contains a mass m0∼−4 ln β and two excited masses m1, m2∼−6 ln β and that m0+4 ln β has a convergent expansion in powers of β. We show that m1, m2 admit convergent expansions of the form −6 ln β+r(β), where r(β) is analytic at β=0. Furthermore, a finite lattice algorithm is given for determining cn, the nth β=0 Taylor coefficient of r(β). Here, cn only depends on a finite number of β=0 Taylor series coefficients of the plaquette–plaquette, plaquette–double plaquette, and double plaquette–double plaquette truncated correlation functions at a finite number of points. For the gauge group Z2, by duality, m1, m2 map to bound states of the low-temperature Ising model; a possible relation between an increasing number of bound states and roughening is discussed.