On Problems of the Lagrangian Quantization of W3-gravity

TL;DR

This paper explores the Lagrangian quantization of W3-gravity using the Batalin-Vilkovisky formalism, revealing a one-parameter non-analytic extension of the gauge algebra and examining solutions in the Sp(2)-covariant formalism.

Contribution

It introduces a one-parametric non-analytic extension of the gauge algebra in W3-gravity and analyzes the existence of solutions in different formalism frameworks.

Findings

Identified a non-analytic extension of the gauge algebra

Constructed a corresponding solution to the classical master equation

Showed non-existence of closed solutions in Sp(2)-covariant formalism up to third order

Abstract

We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin-Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric non-analytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp(2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.