Comments on the Quantum Field Theory of the Coulomb Gas Formalism

 I will revisit the quantum field theory of the Coulomb gas formalism, clarifying several important points along the way. The first key ingredient involves a peculiarity of the timelike linear dilaton: although the background charge Q breaks the scalar field’s continuous shift symmetry, the exponential of the action is still invariant under a discrete shift since Q is imaginary. Gauging this symmetry makes the linear dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to a BRST current first introduced by Felder, and the BRST cohomology singles out the minimal model operators within the linear dilaton theory. The model at radius R=pp′‾‾‾√R=pp′ has two marginal operators corresponding to the Dotsenko-Fateev screening charges. Deforming by them, one obtains a model that might be called a “BRST quotiented compact timelike Liouville theory” with many interesting properties which I will describe. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlators and allows for a kinematic derivation of the fusion rules. In contrast to spacelike Liouville, these resonance correlators are finite because the zero mode is compact.

Date

Affiliation

Member, School of Natural Sciences, IAS

Speakers

Daniel Kapec