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.
Highlights
JHEP01(2022)010 auxiliary Lorentz-vector valued one-form fields that, upon integrating out, yield the desired combination [15,16,17]
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 higherderivative 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
Summary
We can calculate the group-theoretical curvatures which, when set to zero, are the field equations of the Chern-Simons theory. Note that in the infinite flavor case, there is no last equation representing any dynamics which is as expected for a Chern-Simons theory. That we have shown that the infinite-dimensional Lie algebra (2.1) gives rise to a soluble set of equations of the form (1.2), we may discuss the inconsistent truncations and the resulting Chern-Simons-like models of gravity. The Chern-Simons-like models, which we obtain by the truncation of the infinite-dimensional algebra (2.1), are still compatible, but they correspond to a subclass of compatible theories whose spectrum is free from the scalar ghost [17]. This concludes our discussion of the 3D infinite-dimensional Lie algebra underlying the 3D holographic c-theorem
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