Brane box realization of chiral gauge theories in two dimensions

We study type IIA configurations of D4-branes and three kinds of NS5-branes . The D4-brane world-volume has finite extent in three directions,,giving r ise to a two-dimensional low-energy field theory. The models have generical ly (0, 2) supersymmetry. We determine the rules to read off the spectrum an d interactions of the field theory from the brane box configuration data. W e discuss the construction of theories with enhanced (0, 4), (0, 6) and (0, 8) supersymmetry. Using T-duality along the directions in which the D4-bra nes are finite, the configuration can be mapped to D1-branes at C-4/gamma s ingularities, with Gamma an abelian subgroup of SU(4). This provides a rede rivation of the rules in the brane box model. The enhancement of supersymme try has a nice geometrical interpretation in the singularity picture in ter ms of the holonomy group of the four-fold singularity. (C) 1999 Elsevier Sc ience B.V.