The BV-algebra structure of W_3 cohomology

TL;DR

This paper explores the BV-algebra structure of the physical state cohomology in W_3 gravity coupled to matter, revealing a connection to polyvector fields on a complex affine space, advancing understanding of algebraic structures in string theory.

Contribution

It demonstrates that the space of physical states in W_3 gravity forms a BV-algebra with a quotient isomorphic to polyvector fields, linking physical state cohomology to geometric algebra structures.

Findings

Physical state space has BV-algebra structure.

Quotient BV-algebra is isomorphic to polyvector fields.

Results connect W_3 cohomology with geometric algebra.

Abstract

We summarize some recent results obtained in collaboration with J. McCarthy on the spectrum of physical states in $W_3$ gravity coupled to $c=2$ matter. We show that the space of physical states, defined as a semi-infinite (or BRST) cohomology of the $W_3$ algebra, carries the structure of a BV-algebra. This BV-algebra has a quotient which is isomorphic to the BV-algebra of polyvector fields on the base affine space of $SL(3,C)$. Details have appeared elsewhere. [Published in the proceedings of "Gursey Memorial Conference I: Strings and Symmetries," Istanbul, June 1994, eds. G. Aktas et al., Lect. Notes in Phys. 447, (Springer Verlag, Berlin, 1995)]