Chiral gravity, log gravity, and extremal CFT

By A. Maloney, Wei Song, Andrew Strominger. 2009

222 citations recorded by the source corpus.

We show that the linearization of all exact solutions of classical chiral gravity around the ${\mathrm{AdS}}_{3}$ vacuum have positive energy. Nonchiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only stationary, axially symmetric solutions of chiral gravity are BTZ black holes, which have positive energy. It is further shown that classical log gravity---the theory with logarithmically relaxed boundary conditions---has finite asymptotic symmetry generators but is not chiral and hence may be dual at the quantum level to a logarithmic conformal field theories (CFT). Moreover we show that log gravity contains chiral gravity within it as a decoupled charge superselection sector. We formally evaluate the Euclidean sum over geometries of chiral gravity and show that it gives precisely the holomorphic extremal CFT partition function. The modular invariance and integrality of the expansion coefficients of this partition function are consistent with the existence of an exact quantum theory of chiral gravity. We argue that the problem of quantizing chiral gravity is the holographic dual of the problem of constructing an extremal CFT, while quantizing log gravity is dual to the problem of constructing a logarithmic extremal CFT.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/575515885c0cc2c2fd3ca3051208fd4446bc2112

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Citations in the corpus

An analytic Lifshitz black hole (2009, background): “Another recent example where this happens is ‘chiral gravity’ in three dimensions, which has asymptotically AdS solutions as well as various squashed and smushed and wipfed solutions [15].”
The black hole and cosmological solutions in IR modified Hořava gravity (2009, unknown): “This prescription agrees with [31] but disagrees with [32].”
Kerr-CFT and gravitational perturbations (2009, background): “Instead, following recent work on TMG [27] we consider the conserved charges.”
Topologically Massive Gravity and the AdS/CFT Correspondence (2009, background): “At first sight one seems to be free to choose either set of boundary conditions, supposedly leading to a different theory for each possibility [17].”
Massive Gravity (2014, background): “These boundary conditions were further explored in [305, 397], where it was shown that the stressenergy tensor for these boundary conditions are finite and not chiral, giving another indication that the theory could be dual to a logarithmic CFT.”
No dynamics in the extremal Kerr throat (2009, background): “, for periodic boundary conditions), though the same basic effect has recently been discussed in the context of chiral gravity [20].”
Theoretical Aspects of Massive Gravity (2011, unknown): “For more on the subtleties, see [210, 211, 212, 213, 214].”
Umbral Moonshine (2012, methodology): “We refer to [28, 29, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85] for further discussions on the AdS/CFT correspondence and extremal CFT’s.”