Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Categorical Equivalence and the Renormalization Group   In this article we review how categorical equivalences are realized by
renormalization group flow in physical realizations of stacks, derived
categories, and derived schemes. We begin by reviewing the physical realization
of sigma models on stacks, as (universality classes of) gauged sigma models,
and look in particular at properties of sigma models on gerbes (equivalently,
sigma models with restrictions on nonperturbative sectors), and decomposition,
in which two-dimensional sigma models on gerbes decompose into disjoint unions
of ordinary theories. We also discuss stack structures on examples of moduli
spaces of SCFTs, focusing on elliptic curves, and implications of subtleties
there for string dualities in other dimensions. In the second part of this
article, we review the physical realization of derived categories in terms of
renormalization group flow (time evolution) of combinations of D-branes,
antibranes, and tachyons. In the third part of this article, we review how
Landau-Ginzburg models provide a physical realization of derived schemes, and
also outline an example of a derived structure on a moduli spaces of SCFTs.

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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: math
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph