Tautological relations in Hodge field theory

Details Tautological relations in Hodge field theory Tautological relations in Hodge field theory

2007-04-07

arxiv.org/abs/0704.1001v1

Nucl. Phys. B 786 (2007), no. 3, 267--296

Mathematics

Quantum Algebra

35 pages

Scientific paper

10.1016/j.nuclphysb.2007.07.003

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.

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