The Holographic c-theorem and Infinite-dimensional Lie Algebras
arXiv:2110.09542 · doi:10.1007/JHEP01(2022)010
Abstract
We discuss a non-dynamical theory of gravity in three-dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.
arXiv comment16 pages, 1 figure, v2: Typos Corrected, Reference Added, Version appeared in JHEP
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Cited by in corpus (7)
- Higher-curvature Gravities from Braneworlds and the Holographic c-theorem
- Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
- 3D Lovelock Gravity and the Holographic c-Theorem
- Nonlocal Massive Gravity from Einstein Gravity
- Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
- Chern-Simons-Like Formulation of Exotic Massive 3D Gravity Models
- Aspects of three-dimensional higher-curvature gravities