Operator algebra of the 4D W_3 string.pdf

a r X i v : h e p - t h / 9 5 0 9 1 2 1 v 1 2 5 S e p 1 9 9 5 OPERATOR ALGEBRA OF THE 4D W3 STRING Peter BOUWKNEGT 1, Jim McCARTHY 1 and Krzysztof PILCH 2 1 Department of Physics and Mathematical Physics University of Adelaide, Adelaide, SA 5005, Australia 2 Department of Physics and Astronomy University of Southern California Los Angeles, CA 90089-0484, USA ABSTRACT The noncritical 4D W3 string is a model of W3 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,C). To appear in the proceedings of “STRINGS ’95: Future Perspectives in String Theory,” USC, March 13–18, 1995 USC-95/24 ADP-95-47/M39 hep-th/9509121 September 1995 OPERATOR ALGEBRA OF THE 4D W3 STRING Peter BOUWKNEGT and Jim McCARTHY Department of Physics and Mathematical Physics, University of Adelaide Adelaide, SA 5005, Australia E-mail: pbouwkne@physics.adelaide.edu.au, jmccarth@physics.adelaide.edu.au and Krzysztof PILCH Department of Physics and Astronomy, U.S.C. Los Angeles, CA 90089-0484, U.S.A. E-mail: pilch@physics.usc.edu ABSTRACT The noncritical 4DW3 string is a model ofW3 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, C). 1. Introduction This paper is a brief outline of our work, over the past few years, on the W3 algebra: its representation theory; the corresponding s