On the Algebraic Structure of the Holomorphic Anomaly for N=2 Topological Strings

TL;DR

This paper explores the algebraic structure underlying the holomorphic anomaly in N=2 topological strings, deriving special geometry equations from a contact term algebra that encodes background dependence.

Contribution

It introduces a novel contact term algebra framework that explains the special geometry and holomorphic anomaly in twisted N=2 strings.

Findings

Derived special geometry equations from contact algebra

Connected the dilaton to contact terms of operators

Provided an algebraic interpretation of the holomorphic anomaly

Abstract

The special geometry ($(t,{\bar t})$-equations) for twisted $N=2$ strings are derived as consistency conditions of a new contact term algebra. The dilaton appears in the contact terms of topological and antitopological operators. The holomorphic anomaly, which can be interpreted as measuring the background dependence, is obtained from the contact algebra relations.