On the Critical Behavior of D1-brane Theories

We study renormalization-group flow patterns in theories arising on D1-branes in various supersymmetry-breaking backgrounds. We argue that the theory of N D1-branes transverse to an orbifold space can be fine-tuned to flow to the corresponding orbifold conformal field theory in the infrared, for particular values of the couplings and theta angles which we determine using the discrete symmetries of the model. By calculating various nonplanar contributions to the scalar potential in the worldvolume theory, we show that fine-tuning is in fact required at finite N, as would be generically expected. We further comment on the presence of singular conformal field theories (such as those whose target space includes a ``throat'' described by an exactly solvable CFT) in the non-supersymmetric context. Throughout the analysis two applications are considered: to gauge theory/gravity duality and to linear sigma model techniques for studying worldsheet string theory.