Abstract
We consider the SO(4,1)-covariant fuzzy hyperboloid Hn4 as a solution of Yang–Mills matrix models, and study the resulting higher-spin gauge theory. The degrees of freedom can be identified with functions on classical H4 taking values in a higher-spin algebra associated to so(4,1), truncated at spin n. We develop a suitable calculus to classify the higher-spin modes, and show that the tangential modes are stable. The metric fluctuations encode one of the spin 2 modes, however they do not propagate in the classical matrix model. Gravity is argued to arise upon taking into account induced gravity terms. This formalism can be applied to the cosmological FLRW space-time solutions of [1], which arise as projections of Hn4. We establish a one-to-one correspondence between the tangential fluctuations of these spaces.
Highlights
In the present paper we continue the exploration of 4-dimensional covariant fuzzy spaces and their associated higher-spin gauge theories, as started in [2,3]
In previous work [2,3], gauge theory on the fuzzy 4-sphere SN4 was studied in detail, starting from the observation that SN4 is a solution of Yang–Mills matrix models supplemented by a mass term, cf. [6]
In this article we provide a careful and detailed analysis of the fluctuation modes on fuzzy Hn4 as a background in Yang–Mills matrix models, focusing mainly on the semi-classical case
Summary
In the present paper we continue the exploration of 4-dimensional covariant fuzzy spaces and their associated higher-spin gauge theories, as started in [2,3]. These are non-commutative spaces which allow to reconcile a quantum structure of space(-time) with covariance under the maximal isometry. Taken as background solution in matrix models, such as the IKKT model, one obtains a higher-spin gauge theory as effective theory around the 4-dimensional covariant fuzzy spaces. Relevant notation and conventions as well as auxiliary identities and derivations are collected in appendices A–D
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