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Gravitational dual of averaged free CFT's over the Narain lattice · Around

2020

Gravitational dual of averaged free CFT's over the Narain lattice

Pérez, Alfredo, Troncoso, Ricardo

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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.

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