Boundary Liouville Field Theory I. Boundary State and Boundary Two-point Function

TL;DR

This paper analyzes boundary Liouville conformal field theory on a disk, providing explicit formulas for bulk and boundary operator expectation values, and discusses applications to the boundary sine-Gordon model.

Contribution

It offers explicit expressions for boundary and bulk operator expectation values in boundary Liouville theory, advancing understanding of boundary conditions and their applications.

Findings

Explicit formulas for bulk operator expectation values.

Explicit formulas for boundary two-point functions.

Discussion of boundary operator properties and applications.

Abstract

Liouville conformal field theory is considered with conformal boundary. There is a family of conformal boundary conditions parameterized by the boundary cosmological constant, so that observables depend on the dimensional ratios of boundary and bulk cosmological constants. The disk geometry is considered. We present an explicit expression for the expectation value of a bulk operator inside the disk and for the two-point function of boundary operators. We comment also on the properties of the degenrate boundary operators. Possible applications and further developments are discussed. In particular, we present exact expectation values of the boundary operators in the boundary sin-Gordon model.