BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings

Authors:	BOUWKNEGT Peter McCARTHY JIM PILCH KRZYSZTOF

Institution:	(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.

Abstract:	Given a simple, simply laced, complex Lie algebra $\mathfrak{g}$ corresponding to the Lie group G, let $\mathfrak{n}_ +$ be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra ${\text{BV}}\mathfrak{g}]$ whose underlying graded commutative algebra is given by the cohomology, with respect to $\mathfrak{n}_ +$ , of the algebra of regular functions on G with values in $\wedge (\mathfrak{n}_ + \backslash \mathfrak{g})$ . We conjecture that ${\text{BV}}\mathfrak{g}]$ describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical $\mathcal{W}\mathfrak{g}]$ string. The conjecture is verified in the two explicitly known cases, $\mathfrak{g} = \mathfrak{s}\mathfrak{l}$ ₂ (the Virasoro string) and $\mathfrak{g} = \mathfrak{s}\mathfrak{l}$ ₃ (the $\mathcal{W}_3$ string).

Keywords:	Batalin-Vilkovisky (BV) algebra cohomology geometry of strings
本文献已被 SpringerLink 等数据库收录！