Semi-infinite forms and topological vertex operator algebras
Abstract
Description
Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type $k<0$ and strong topological vertex partial operads of type $k<0$ are constructed. It is proved that the category of (locally-)grading-restricted (strong) topological vertex operator algebras of type $k<0$ and the category of (weakly) meromorphic ${\Bbb Z}\times {\Bbb Z}$-graded algebras over the (strong) topological vertex partial operad of type k are isomorphic. As an application of this isomorphism theorem, the following conjecture of Lian-Zuckerman and Kimura-Voronov-Zuckerman is proved: A strong topological vertex operator algebra gives a homotopy Gerstenhaber algebra. These results hold in particular for the tensor product of the moonshine module vertex operator algebra, the vertex algebra constructed {from} a rank 2 Lorentz lattice and the ghost vertex operator algebra, studied in detail first by Lian and Zuckerman.
63 pages. LaTeX file. One reference is added and the terminology is slightly revised
63 pages. LaTeX file. One reference is added and the terminology is slightly revised