Equivariant holomorphic anomaly equation

Abstract

In [16] the fundamental relationship between stable quotient invariants and the B-model for local P2 in all genera was studied under some specialization of equivariant variables. We generalize the argument of [16] to full equivariant settings without the specialization. Our main results are the proof of holomorphic anomaly equations for the equivariant Gromov-Witten theories of local P2 and local P3. We also state the generalization to full equivariant formal quintic theory of the result in [17].

58 pages, new results for KP3 are included, the contents in arXiv:1807.05501 are included in Appendix, arXiv admin note: substantial text overlap with arXiv:1702.06096, arXiv:1803.01409, arXiv:1804.04399