Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrability of $\mathcal W({\mathfrak{sl}_d})$-symmetric Toda
  conformal field theories I : Quantum geometry   In this article which is the first of a series of three, we consider
$\mathcal W({\mathfrak{sl}_d})$-symmetric conformal field theory in topological
regimes for a generic value of the background charge, where $\mathcal
W({\mathfrak{sl}_d})$ is the W-algebra associated to the affine Lie algebra
$\widehat{\mathfrak{sl}_d}$, whose vertex operator algebra is included to that
of the affine Lie algebra $\widehat{\mathfrak g}_1$ at level 1. In such
regimes, the theory admits a free field representation. We show that the
generalized Ward identities assumed to be satisfied by chiral conformal blocks
with current insertions can be solved perturbatively in topological regimes.
This resolution uses a generalization of the topological recursion to
non-commutative, or quantum, spectral curves. In turn, special geometry
arguments yields a conjecture for the perturbative reconstruction of a
particular chiral block.

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The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: eess