D Branes from Liouville Strings

We develop quantization aspects of our Liouville approach to noncritical strings, proposing a path-integral formulation of a second quantization of string theory, that incorporates naturally the couplings of string sources to background fields. Such couplings are characteristic of macroscopic string solutions and/or D-brane theories. Resummation over world-sheet genera in the presence of stringy (σ-model) soliton backgrounds, and recoil effects associated with logarithmic operators on the world sheet, play a crucial role in inducing such sources as well-defined renormalization-group counterterms. Using our Liouville renormalization group approach, we derive the appropriate second-order equation of motion for the D brane. We discuss within this approach the appearance of open strings, whose ends carry nontrivial Chan–Paton-like quantum numbers related to the W∞ charges of two-dimensional string black holes.