On the critical behavior of D1-brane theories

The authors study renormalization-group of patterns in theories arising on D1-branes in various supersymmetry-breaking backgrounds. The authors 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 θ angles which the authors determine using the discrete symmetries of the model. By calculating various nonplanar contributions to the scalar potential in the world volume theory, the authors show that fine-tuning is in fact required at finite N, as would be generically expected. The authors 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