Studies of chiral symmetry breaking in SU(2) lattice gauge theory

Abstract

We study chiral symmetry breaking ( χSB) in SU(2) lattice gauge theory with quarks in the l = 1 2 , l = 1, l = 3 2 , and l = 2 representations of the color group. We perform Monte Carlo evaluations of 〈 ψψ〉 in the quenched approximation and extract the relevant length scales for χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain T l = 1/T l = 1 2 ∼ 8 . Our results for the higher representations, l = 3 2 and l = 2 , are consistent with Casimir scaling and give C 2 g mom 2 ∼ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.