Chiral ring in the 4D W_3 string (hep-th title)
(or Operator algebra of the D=2+2 W-string (title in journal))
J. McCarthy
ADP-95-21/M30, hep-th/9509134, in Confronting the Infinite, eds. A.L. Carey, W.J. Ellis, P.A. Pearce and A.W. Thomas (World Scientific, Singapore, 1995), pp. 123-135. [Paper presented at Confronting the Infinite - A conference held in honour of Professors Bert Green and Angas Hurst, Adelaide, 14-17 Feb 1994.]

I summarize some recent results obtained in collaboration with P. Bouwknegt and K. Pilch on the spectrum of physical states in W_3 gravity coupled to c=2 matter. In particular, it is shown that the algebra of operators corresponding to physical states -- defined as a semi-infinite (or BRST) cohomology of the W_3 algebra -- carries the structure of a G-algebra. This G-algebra has a quotient which is isomorphic to the G-algebra of polyvector fields on the base affine space of SL(3,C). Details have appeared elsewhere.

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