Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational dual of averaged free CFT's over the Narain lattice   It has been recently argued that the averaging of free CFT's over the Narain
lattice can be holographically described through a Chern-Simons theory for
$U\left(1\right)^{D}\times U\left(1\right)^{D}$ with a precise prescription to
sum over three-dimensional handlebodies. We show that a gravitational dual of
these averaged CFT's would be provided by Einstein gravity on AdS$_{3}$ with
$U\left(1\right)^{D-1}\times U\left(1\right)^{D-1}$ gauge fields, endowed with
a precise set of boundary conditions closely related to the "soft hairy" ones.
Gravitational excitations then go along diagonal $SL\left(2,\mathbb{R}\right)$
generators, so that the asymptotic symmetries are spanned by
$U\left(1\right)^{D}\times U\left(1\right)^{D}$ currents. The stress-energy
tensor can then be geometrically seen as composite of these currents through a
twisted Sugawara construction. Our boundary conditions are such that for the
reduced phase space, there is a one-to-one map between the configurations in
the gravitational and the purely abelian theories. The partition function in
the bulk could then also be performed either from a non-abelian Chern-Simons
theory for two copies of $SL\left(2,\mathbb{R}\right)\times
U\left(1\right)^{D-1}$ generators, or formally through a path integral along
the family of allowed configurations for the metric. The new boundary
conditions naturally accommodate BTZ black holes, and the microscopic number of
states then appears to be manifestly positive and suitably accounted for from
the partition function in the bulk. The inclusion of higher spin currents
through an extended twisted Sugawara construction in the context of higher spin
gravity is also briefly addressed.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th