Chiral Symmetry Breaking in Strongly Coupled 1 + 1 Dimensional Lattice Gauge Theories 1

1. Abstract We analyse − within the hamiltonian formalism with staggered fermions − the patterns of chiral symmetry breaking for the strongly coupled Schwinger and U (N c)-color 't Hooft models with one and two flavor of fermions. Using the correspondence between these strongly coupled gauge models and antiferromagnetic spin chains, we provide a rather intuitive picture of their ground states, elucidate their patterns of chiral symmetry breaking, and compute the pertinent chiral condensates. Our analysis evidences an intriguing relationship between the values of the lattice chiral condensates of the 't Hooft and Schwinger models with one flavor of fermions. 2. Introduction Confinement and chiral symmetry breaking go hand in hand as strong coupling phenomena in a gauge theory; while confinement is an observed property of the strong interactions and it is an unproven, but widely believed feature of most non-Abelian gauge theories in four and lower space-time dimensions, chiral symmetry is only an approximate symmetry of particle physics since the up and down quarks are light but not massless. The strong coupling limit of lattice gauge theories, even if far from the scaling regime, is useful to study interesting properties of a gauge model. In this limit, the gauge theory exhibits confinement and dynamical chiral symmetry breaking: Wilson fermions explicitly break chiral symmetry while for staggered fermions, even if the continuous chiral symmetry is broken 1 Contribution to the proceedings of the workshop " Lattice fermions and the structure of the vacuum " , 5-9 October 1999, Dubna, Russia.