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Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation

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Abstract:

We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov–Witten invariants via tau-function of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity.

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Authors and Affiliations

  1. SISSA, Via Beirut 2–4, 34014 Trieste, Italy. E-mail: dubrovin@sissa.it, , , , , , IT

    Boris Dubrovin

  2. Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.¶E-mail: youjin@kusm.kyoto-u.ac.jp, , , , , , JP

    Youjin Zhang

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  1. Boris Dubrovin
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  2. Youjin Zhang
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Received: 16 January 1998 / Accepted: 2 April 1998

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Dubrovin, B., Zhang, Y. Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation. Comm Math Phys 198, 311–361 (1998). https://doi.org/10.1007/s002200050480

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  • DOI: https://doi.org/10.1007/s002200050480

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