Weyl Degree of Freedom in The Nambu-Goto String Through Field Transformation

TL;DR

This paper explores how Weyl degrees of freedom can be incorporated into the Nambu-Goto string using path integral methods, gauge fixing, and BRST transformations, linking different string formulations.

Contribution

It introduces a method to embed Weyl degrees of freedom in the Nambu-Goto string via field transformations and gauge choices, connecting conformal and light-cone gauges.

Findings

Weyl degrees of freedom are introduced using reparametrization invariant measure.

The transition from conformal to light-cone gauge is achieved through finite field dependent BRST transformation.

The generating functional in light-cone gauge is derived from the conformal gauge formulation.

Abstract

We show how Weyl degrees of freedom, can be introduced in the Nambu-Goto string in the path integral formulation using reparametrization invariant measure. We first identify Weyl degrees in conformal gauge using BFV formulation. Further we change Nambu-Goto string action to Polyakov action. The generating functional in light-cone gauge is then obtained from the generating func- tional corresponding to Polyakov action in conformal gauge by using suitably constructed finite field dependent BRST transformation.