On recursion relations in topological string theory

Abstract

We discuss a link between the topological recursion relations derived algebraically by Witten and the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. This is obtained through the definition of an operator ${\mathcal{W}}_s$ that reproduces the recursion relations for topological string theory coupled to worldsheet gravity a la BCOV. This operator is contained inside an algebra that generalizes the tt* equations and whose direct consequence is the holomorphic anomaly equation itself.

v3: matches the version to appear on JHEP

References in corpus (3)

• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• Holomorphic Anomalies in Topological Field Theories
• On the Algebraic Structure of the Holomorphic Anomaly for N=2 Topological Strings