A Fock Sheaf For Givental Quantization
作者： Tom Coates , Hiroshi Iritani
DOI: 10.1215/21562261-2017-0036
关键词: Holomorphic function 、 Algebra 、 Mathematics 、 Frobenius manifold 、 Quantum cohomology 、 Derived category 、 Modular form 、 Fock space 、 Orbifold 、 Sheaf 、 Pure mathematics
摘要: We give a global, intrinsic, and co-ordinate-free quantization formalism for Gromov-Witten invariants their B-model counterparts, which simultaneously generalizes the formalisms described by Witten, Givental, Aganagic-Bouchard-Klemm. Descendant potentials live in Fock sheaf, consisting of local functions on Givental's Lagrangian cone that satisfy (3g-2)-jet condition Eguchi-Xiong; they also certain anomaly equation, Holomorphic Anomaly Equation Bershadsky-Cecotti-Ooguri-Vafa. interpret formula higher-genus associated to semisimple Frobenius manifold this setting, showing that, case, there is canonical global section sheaf. This automatically has modularity properties. When X variety with quantum cohomology, theorem Teleman implies coincides geometric descendant potential defined X. use our prove version Ruan's Crepant Transformation Conjecture compact toric orbifolds. combined earlier joint work Jiang, shows total orbifold modular function group autoequivalences derived category
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