Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-08-09
Commun.Math.Phys.177:305-326,1996
Physics
High Energy Physics
High Energy Physics - Theory
phyzzx.tex, MIT-CTP-2346
Scientific paper
10.1007/BF02101895
We construct a Batalin-Vilkovisky (BV) algebra on moduli spaces of Riemann surfaces. This algebra is background independent in that it makes no reference to a state space of a conformal field theory. Conformal theories define a homomorphism of this algebra to the BV algebra of string functionals. The construction begins with a graded-commutative free associative algebra $\C$ built from the vector space whose elements are orientable subspaces of moduli spaces of punctured Riemann surfaces. The typical element here is a surface with several connected components. The operation $\Delta$ of sewing two punctures with a full twist is shown to be an odd, second order derivation that squares to zero. It follows that $(\C, \Delta)$ is a Batalin-Vilkovisky algebra. We introduce the odd operator $\delta = \partial + \hbar\Delta$, where $\partial$ is the boundary operator. It is seen that $\delta^2=0$, and that consistent closed string vertices define a cohomology class of $\delta$. This cohomology class is used to construct a Lie algebra on a quotient space of $\C$. This Lie algebra gives a manifestly background independent description of a subalgebra of the closed string gauge algebra.
Sen Ashoke
Zwiebach Barton
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