Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fock Sheaf For Givental Quantization   We give a global, intrinsic, and co-ordinate-free quantization formalism for
Gromov-Witten invariants and their B-model counterparts, which simultaneously
generalizes the quantization formalisms described by Witten, Givental, and
Aganagic-Bouchard-Klemm. Descendant potentials live in a Fock sheaf, consisting
of local functions on Givental's Lagrangian cone that satisfy the (3g-2)-jet
condition of Eguchi-Xiong; they also satisfy a certain anomaly equation, which
generalizes the Holomorphic Anomaly Equation of Bershadsky-Cecotti-Ooguri-Vafa.
We interpret Givental's formula for the higher-genus potentials associated to a
semisimple Frobenius manifold in this setting, showing that, in the semisimple
case, there is a canonical global section of the Fock sheaf. This canonical
section automatically has certain modularity properties. When X is a variety
with semisimple quantum cohomology, a theorem of Teleman implies that the
canonical section coincides with the geometric descendant potential defined by
Gromov-Witten invariants of X. We use our formalism to prove a higher-genus
version of Ruan's Crepant Transformation Conjecture for compact toric
orbifolds. When combined with our earlier joint work with Jiang, this shows
that the total descendant potential for compact toric orbifold X is a modular
function for a certain group of autoequivalences of the derived category of X.

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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph