BibTex format
@unpublished{Coates:2014,
author = {Coates, T and Iritani, H},
title = {A Fock Sheaf For Givental Quantization},
url = {http://arxiv.org/abs/1411.7039v2},
year = {2014}
}
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Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - We give a global, intrinsic, and co-ordinate-free quantization formalism forGromov-Witten invariants and their B-model counterparts, which simultaneouslygeneralizes the quantization formalisms described by Witten, Givental, andAganagic-Bouchard-Klemm. Descendant potentials live in a Fock sheaf, consistingof local functions on Givental's Lagrangian cone that satisfy the (3g-2)-jetcondition of Eguchi-Xiong; they also satisfy a certain anomaly equation, whichgeneralizes the Holomorphic Anomaly Equation of Bershadsky-Cecotti-Ooguri-Vafa.We interpret Givental's formula for the higher-genus potentials associated to asemisimple Frobenius manifold in this setting, showing that, in the semisimplecase, there is a canonical global section of the Fock sheaf. This canonicalsection automatically has certain modularity properties. When X is a varietywith semisimple quantum cohomology, a theorem of Teleman implies that thecanonical section coincides with the geometric descendant potential defined byGromov-Witten invariants of X. We use our formalism to prove a higher-genusversion of Ruan's Crepant Transformation Conjecture for compact toricorbifolds. When combined with our earlier joint work with Jiang, this showsthat the total descendant potential for compact toric orbifold X is a modularfunction for a certain group of autoequivalences of the derived category of X.
AU - Coates,T
AU - Iritani,H
PY - 2014///
TI - A Fock Sheaf For Givental Quantization
UR - http://arxiv.org/abs/1411.7039v2
ER -