D-branes in non-critical superstrings and minimal super-Yang-Mills in various dimensions

We construct and analyze D-branes in superstring theories in even dimensions less than ten. The backgrounds under study are supersymmetric Rd−1,1×SL(2,R)k/U(1) where the level of the supercoset is tuned such as to provide bona fide string theory backgrounds. We provide exact boundary states for D-branes that are localized at the tip of the cigar SL(2,R)/U(1) supercoset conformal field theory. We analyze the spectra of open strings on these D-branes and show explicitly that they are consistent with supersymmetry in d=2,4 and 6. The low energy theory on the world-volume of the D-brane in each case is pure Yang-Mills theory with minimal supersymmetry. In the case with four macroscopic flat directions d=4, we realize an N=1 super-Yang-Mills theory, and we interpret the backreaction for the dilaton as the running of the gauge coupling, and study the relation between R-symmetry breaking in the gauge theory and the backreaction on the RR axion.