Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lightcone Modular Bootstrap and Pure Gravity   We explore the large spin spectrum in two-dimensional conformal field
theories with a finite twist gap, using the modular bootstrap in the lightcone
limit. By recursively solving the modular crossing equations associated to
different $PSL(2,\mathbb{Z})$ elements, we identify the universal contribution
to the density of large spin states from the vacuum in the dual channel. Our
result takes the form of a sum over $PSL(2,\mathbb{Z})$ elements, whose leading
term generalizes the usual Cardy formula to a wider regime. Rather curiously,
the contribution to the density of states from the vacuum becomes negative in a
specific limit, which can be canceled by that from a non-vacuum Virasoro
primary whose twist is no bigger than $c-1\over16$. This suggests a new upper
bound of $c-1\over 16$ on the twist gap in any $c>1$ compact, unitary conformal
field theory with a vacuum, which would in particular imply that pure AdS$_3$
gravity does not exist. We confirm this negative density of states in the pure
gravity partition function by Maloney, Witten, and Keller. We generalize our
discussion to theories with $\mathcal{N}=(1,1)$ supersymmetry, and find similar
results.

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The categories of this paper are: econ
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys