BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings |
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Authors: | BOUWKNEGT Peter McCARTHY JIM PILCH KRZYSZTOF |
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Affiliation: | (1) Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, SA, 5005, Australia;(2) Department of Pnysics and Astronomy, University of Southern California, Los Angeles, CA, 90089-0484, U.S.A. |
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Abstract: | Given a simple, simply laced, complex Lie algebra corresponding to the Lie group G, let be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra whose underlying graded commutative algebra is given by the cohomology, with respect to , of the algebra of regular functions on G with values in . We conjecture that describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical string. The conjecture is verified in the two explicitly known cases,2 (the Virasoro string) and 3 (the string). |
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Keywords: | Batalin-Vilkovisky (BV) algebra cohomology geometry of strings. |
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