2017/06/29 by Caldararu, Andrei, Tu, Junwu · 1 citation
#14J33 #14K25 #14N35 #16E40 #53D37 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1706.09912
We compute the g=1, n=1 B-model Gromov-Witten invariant of an elliptic curve E directly from the derived category D(E). More precisely, we carry out the computation of the categorical Gromov-Witten invariant defined by Costello using as target a cyclic A_∞ model of D(E) described by Polishchuk. This is the first non-trivial computation of a positive genus categorical Gromov-Witten invariant, and the result agrees with the prediction of mirror symmetry: it matches the classical (non-categorical) Gromov-Witten invariants of a symplectic 2-torus computed by Dijkgraaf.