Operator Formalism for Bosonic Beta-Gamma Fields on General Algebraic Curves

TL;DR

This paper develops an operator formalism for bosonic beta-gamma systems on algebraic curves, generalizing previous models on the complex sphere, and provides explicit algebraic and correlation function computations.

Contribution

It introduces a new operator formalism for beta-gamma systems on arbitrary algebraic curves, extending existing models beyond the complex sphere.

Findings

Explicit algebraic realization in a Hilbert space.

Detailed two and four-point correlation function computations.

Generalization of the gaussian representation to algebraic curves.

Abstract

An operator formalism for bosonic $\beta-\gamma$ systems on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra formed by the fields is given in a Hilbert space equipped with a bilinear form. The construction is based on the "gaussian" representation for $\beta-\gamma$ systems on the complex sphere [Alvarez-Gaum\' e et al, Nucl. Phys. B 311 (1988) 333]. Detailed computations are provided for the two and four points correlation functions.