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Tautological relations in Hodge field theory


Losev, A; Shadrin, S; Shneiberg, I (2007). Tautological relations in Hodge field theory. Nuclear Physics. Section B, 786(3):267-296.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:15 Dec 2009 12:52
Last Modified:06 Dec 2017 20:43
Publisher:Elsevier
ISSN:0550-3213
Publisher DOI:https://doi.org/10.1016/j.nuclphysb.2007.07.003
Related URLs:http://arxiv.org/abs/0704.1001

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