Pauli-Villars' regularization of ghosts in path-integral string formulation

TL;DR

This paper investigates how Pauli-Villars regulators can be used to preserve conformal invariance in the path-integral formulation of string theory, ensuring consistent quantization of the Nambu-Goto string.

Contribution

It demonstrates the preservation of conformal invariance using Pauli-Villars regulators and calculates their effects on the effective action and central charge in string quantization.

Findings

Regulators preserve conformal invariance in path-integral string formulation

Effective action and central charge are consistent with mean-field quantization

Higher-derivative corrections are briefly analyzed for different regularizations

Abstract

I consider Pauli-Villars' regulators for the ghosts in the path-integral string formulation and show how they preserve conformal invariance. I calculate the regulator contributions to the effective action and to the central charge and demonstrate the consistency of the mean-field quantization of the Nambu-Goto string in $2<d\leq26$. The higher-derivative corrections to the Liouville action are briefly considered for the Pauli-Villars and proper-time regularizations.