Chiral gravity, log gravity, and extremal CFT

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.064007· OSTI ID:21413416

Maloney, Alexander ^[1]; Wei, Song ^[2]; Strominger, Andrew ^[3]

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1. Physics Department, McGill University, Montreal, QC H3A 2T8 (Canada)
2. Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190 (China)
3. Center for the Fundamental Laws of Nature Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138 (United States)

We show that the linearization of all exact solutions of classical chiral gravity around the AdS{sub 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.

• OSTI ID: 21413416
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 6; Other Information: DOI: 10.1103/PhysRevD.81.064007; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTI DE SITTER SPACE
ASYMPTOTIC SOLUTIONS
AXIAL SYMMETRY
BLACK HOLES
BOUNDARY CONDITIONS
CHIRALITY
CONFORMAL INVARIANCE
EQUATIONS OF MOTION
EUCLIDEAN SPACE
EXACT SOLUTIONS
FIELD THEORIES
GRAVITATION
HOLOGRAPHY
INSTABILITY
PARTITION FUNCTIONS
QUANTUM FIELD THEORY
SPECTRA
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
RIEMANN SPACE
SPACE
SYMMETRY