Tautological relations in Hodge field theory

Abstract

We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invariants to Gromov-Witten invariants. It generalizes the Barannikov-Kontsevich construction to the case of higher genera correlators with gravitational descendants. We prove the main theorem stating that algebraically defined Hodge field theory correlators satisfy all tautological relations. From this perspective the statement that Barannikov-Kontsevich construction provides a solution of the WDVV equation looks as the simplest particular case of our theorem. Also it generalizes the particular cases of other low-genera tautological relations proven in our earlier works; we replace the old technical proofs by a novel conceptual proof.

35 pages

References in corpus (5)

• Tautological relations and the r-spin Witten conjecture
• An algebro-geometric proof of Witten's conjecture
• Enumerative tropical algebraic geometry in R2
• A simple proof of Witten conjecture through localization
• BFV-complex and higher homotopy structures

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• Anomaly cancellation in the topological string
• Renormalization Method and Mirror Symmetry
• Variation of Hodge structures, Frobenius manifolds and Gauge theory
• $N=1$ formal genus $0$ Gromov-Witten theories and Givental's formalism
• Generalized cohomological field theories in the higher order formalism