Operator algebra of the 4D W_3 string

TL;DR

This paper explores the BRST quantization of the 4D W_3 string, revealing its physical operators form a BV-algebra modeled on polyvector fields, advancing understanding of higher-dimensional string theories.

Contribution

It introduces a novel BV-algebra structure for the 4D W_3 string's physical operators, extending the algebraic framework of string quantization to four dimensions.

Findings

Physical operators form a BV-algebra.

BV-algebra modeled on polyvector fields on SL(3,C).

Provides a foundation for 4D W_3 string quantization.

Abstract

The noncritical $4D$ $\cW_3$ string is a model of $\cW_3$ gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the $2D$ (Virasoro) string. The physical operators form a BV-algebra. We model this BV-algebra on that of the polyderivations of a commutative ring on six variables with a quadratic constraint, or, equivalently, on the BV-algebra of (polynomial) polyvector fields on the base affine space of $SL(3,\CC)$. Details have appeared elsewhere. To appear in the proceedings of ``STRINGS '95: Future Perspectives in String Theory,'' USC, March 13--18, 1995