Glueball mass spectrum and mass splitting in 2+1 strongly coupled lattice gauge theories

Abstract

For a 2+1 strongly coupled (β=2/g ² small) Wilson action lattice gauge theory with complex character we analyze the mass spectrum of the associated quantum field theory restricted to the subspace generated by the plaquette function and its complex conjugate. It is shown that there is at least one but not more than two isolated masses and each mass admits a representation of the formm(β)=−4lnβ+r(β), wherer(β) is a gauge group representation dependent function analytic inβ ^1/2 orβ atβ=0. For the gauge group SU(3) there is mass splitting and the two massesm _± are given by

$$m_ \pm (\beta ) = - 41n\beta + 16r^4 + \tfrac{1}{2}(2 \pm 1)\beta + \left( {d_ \pm (\beta )\sum\limits_{n = 2}^\infty {c_n^ \pm } \beta ^n } \right)$$

wherer=3 is the dimension of the representation andd _±(β) is analytic atβ=0.c ^± _n can be determined from a finite number of theβ=0 Taylor series coefficients of finite lattice truncated plaquette-plaquette correlation function at a finite number of points.