Blowup Equations and Holomorphic Anomaly Equations

2021/12/29 by Sun, Kaiwen
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2112.14753

Abstract

Blowup equations and holomorphic anomaly equations are two universal yet completely different approaches to solve refined topological string theory on local Calabi-Yau threefolds corresponding to A- and B-model respectively. The former originated from comparing Nekrasov partition functions of 4d N=2 gauge theories on Ω defomed spacetime ℂ²_ε1,ε2 and its one-point blown-up, while the latter takes root in the degeneration of wordsheet Riemann surfaces. The relation between the two approaches is an open question. In this short note, we find a novel recursive equation governing their consistency, which we call the consistency equation. This new equation computes the modular anomaly of blowup equations order by order. The consistency equation also suggests a non-holomorphic extension of blowup equations.

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