BCOV theory via Givental group action on cohomological field theories

Abstract

In a previous paper (arXiv:0704.1001), Losev, me, and Shneiberg constructed a full descendant potential associated to an arbitrary cyclic Hodge dGBV algebra. This contruction extended the construction of Barannikov and Kontsevich of solution of the WDVV equation, based on the earlier paper of Bershadsky, Cecotti, Ooguri, and Vafa. In the present paper, we give an interpretation of this full descendant potential in terms of Givental group action on cohomological field theories. In particular, the fact that it satisfies all tautological equations becomes a trivial observation.

22 pages

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Cited by in corpus (25)

• Identification of the Givental formula with the spectral curve topological recursion procedure
• A polynomial bracket for the Dubrovin--Zhang hierarchies
• Double ramification cycles and integrable hierarchies
• A new cohomology class on the moduli space of curves
• On deformations of quasi-Miura transformations and the Dubrovin-Zhang bracket
• Dubrovin's superpotential as a global spectral curve
• Equivalence of ELSV and Bouchard-Mariño conjectures for $r$-spin Hurwitz numbers
• Givental graphs and inversion symmetry
• Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebras
• A group action on Losev-Manin cohomological field theories
• Hypercommutative operad as a homotopy quotient of BV
• Deformation theory of Cohomological Field Theories
• The tautological ring of ${\mathcal{M}}_{g,n}$ via Pandharipande-Pixton-Zvonkine $r$-spin relations
• Renormalization Method and Mirror Symmetry
• Variation of Hodge structures, Frobenius manifolds and Gauge theory
• Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks
• Gromov-Witten invariants of ${\mathbb{P}}^1$ coupled to a KdV tau function
• Towards Lax formulation of integrable hierarchies of topological type
• A Landau-Ginzburg mirror theorem via matrix factorizations
• SL(2,C) group action on Cohomological field theories
• $N=1$ formal genus $0$ Gromov-Witten theories and Givental's formalism
• Cohomological field theories with non-tautological classes
• Open topological recursion relations in genus $1$ and integrable systems
• Generalized cohomological field theories in the higher order formalism
• Cut-and-join operators in cohomological field theory and topological recursion