The Holographic c-theorem and Infinite-dimensional Lie Algebras

TL;DR

This paper explores a non-dynamical 3D gravity theory based on an infinite-dimensional Lie algebra, revealing connections to higher-derivative gravity models consistent with the holographic c-theorem and extending these ideas to higher dimensions.

Contribution

It introduces a novel algebraic framework linking infinite-dimensional Lie algebras to holographic c-theorem compatible gravity models, including new insights into truncations and higher-dimensional extensions.

Findings

Truncations of the algebra reproduce 3D massive gravity models.

Higher-dimensional truncations yield known c-theorem consistent gravity models.

The approach connects algebraic structures to holographic principles in gravity.

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.