Strings in Noncompact Spacetimes: Boundary Terms and Conserved Charges

TL;DR

This paper explores how boundary terms in noncompact conformal field theories influence string theory, leading to new formulas for conserved charges like ADM energy-momentum directly from CFT principles.

Contribution

It introduces a novel approach to defining conserved charges in string theory via boundary terms in noncompact CFTs, connecting boundary operator correlators to spacetime physics.

Findings

One-point functions on the sphere relate to boundary spacetime terms.

Boundary operators on the disk do not vanish, but correspond to boundary spacetime terms.

Derived formulas for conserved gauge charges, including ADM energy-momentum, from CFT boundary terms.

Abstract

We study some of the novel properties of conformal field theories with noncompact target spaces as applied to string theory. Standard CFT results get corrected by boundary terms in the target space in a way consistent with the expected spacetime physics. For instance, one-point functions of general operators on the sphere and boundary operators on the disk need not vanish; we show that they are instead equal to boundary terms in spacetime. By applying this result to vertex operators for spacetime gauge transformations with support at infinity, we derive formulas for conserved gauge charges in string theory. This approach provides a direct CFT definition of ADM energy-momentum in string theory.