A B-twisted Landau-Ginzburg model plus topological gravity on the worldsheet is shown to be the exact dual of any interacting one-matrix model, with matrix traces mapping directly to vertex operators and correlators agreeing to all orders in genus and 't Hooft coupling.
Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Bershadsky-Cecotti-Ooguri-Vafa (BCOV) proposed that the B-model of mirror symmetry should be described by a quantum field theory on a Calabi-Yau variety, which they called the Kodaira-Spenser theory (we call it the BCOV theory). This is the first of three papers in which we construct and analyze the quantum BCOV theory. In this paper, we construct the classical field theory on a Calabi-Yau variety of arbitrary dimension; define what it means to give a quantization; analyze the relation Givental's symplectic formalism for Gromov-Witten theory; prove uniqueness of the quantization on an elliptic curve; and prove the Virasoro constraints on an elliptic curve. The second paper (arXiv:1112.4063) proves that the partition function of the quantum BCOV theory on the elliptic curve is equivalent to the Gromov-Witten theory of the mirror elliptic curve. The third paper, in progress, constructs the quantum BCOV theory on a general Calabi-Yau.
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B-model CEI on Calabi-Yau 3-folds satisfy holomorphic anomaly equations after proving dilaton/string/divisor analogs and applying Givental quantization.
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Worldsheet Duals to One-Matrix Models
A B-twisted Landau-Ginzburg model plus topological gravity on the worldsheet is shown to be the exact dual of any interacting one-matrix model, with matrix traces mapping directly to vertex operators and correlators agreeing to all orders in genus and 't Hooft coupling.
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B-model Categorical Enumerative Invariants and holomorphic anomaly equations
B-model CEI on Calabi-Yau 3-folds satisfy holomorphic anomaly equations after proving dilaton/string/divisor analogs and applying Givental quantization.