Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proving the equivalence of $c$-extremization and its gravitational dual
  for all toric quivers   The gravitational dual of $c$-extremization for a class of $(0,2)$
two-dimensional theories obtained by twisted compactifications of D3-brane
gauge theories living at a toric Calabi-Yau three-fold has been recently
proposed. The equivalence of this construction with $c$-extremization has been
checked in various examples and holds also off-shell. In this note we prove
that such equivalence holds for an arbitrary toric Calabi-Yau. We do it by
generalizing the proof of the equivalence between $a$-maximization and volume
minimization for four-dimensional toric quivers. By an explicit
parameterization of the R-charges we map the trial right-moving central charge
$c_r$ into the off-shell functional to be extremized in gravity. We also
observe that the similar construction for M2-branes on $\mathbb{C}^4$ is
equivalent to the $\mathcal{I}$-extremization principle that leads to the
microscopic counting for the entropy of magnetically charged black holes in
AdS$_4\times S^7$. Also this equivalence holds off-shell.

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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: physics