D Branes from Liouville Strings

TL;DR

This paper develops a second quantization framework for non-critical string theory using Liouville methods, incorporating D-branes and background couplings, and deriving equations of motion for D-branes with implications for open strings and black hole charges.

Contribution

It introduces a path-integral second quantization approach for Liouville non-critical strings, including D-branes and background interactions, with a focus on renormalization and recoil effects.

Findings

Derived second-order equations of motion for D-branes.

Connected open string endpoints to W_infinity charges of 2D black holes.

Presented a path-integral formulation incorporating string sources and backgrounds.

Abstract

We develop quantization aspects of our Liouville approach to non-critical 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 ($\sigma$-model) soliton backgrounds, and recoil effects associated with logarithmic operators on the world sheet, play a crucial r\^ole 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 non-trivial Chan-Paton-like quantum numbers related to the $W_\infty$ charges of two-dimensional string black holes.