2020/09/14 by Caldararu, Andrei, Tu, Junwu
#14N35 #53D45 #57K20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2009.06659
To a pair (A,s) consisting of a smooth, cyclic A_∞-algebra A and a splitting s of the Hodge filtration on its Hochschild homology Costello (2005) associates an invariant which conjecturally generalizes the total descendant Gromov-Witten potential of a symplectic manifold. In this paper we give explicit, computable formulas for Costello's invariants, as Feynman sums over partially directed stable graphs. The formulas use in a crucial way the combinatorial string vertices defined earlier by Costello and the authors. Explicit computations elsewhere confirm in many cases the equality of categorical invariants with known Gromov-Witten, Fan-Jarvis-Ruan-Witten, and Bershadsky-Cecotti-Ooguri-Vafa invariants.