Higher Spins without (Anti-)de Sitter

Abstract

Can the holographic principle be extended beyond the well-known AdS/CFT correspondence? During the last couple of years, there has been a substantial amount of research trying to find answers for this question. In this work, we provide a review of recent developments of three-dimensional theories of gravity with higher spin symmetries. We focus in particular on a proposed holographic duality involving asymptotically flat spacetimes and higher spin extended bms 3 symmetries. In addition, we also discuss developments concerning relativistic and nonrelativistic higher spin algebras. As a special case, Carroll gravity will be discussed in detail.

Carrollian and Galilean conformal higher-spin algebras in any dimensions

“…Alternative contractions of higher-spin algebras in three-dimensions were already considered in [144] and our techniques should allow one to identify those that admit a realisations as quotients of the universal enveloping algebra of the isometries of a given spatially isotropic spacetime [143]. Some of these three-dimensional algebras have been already exploited to set up non-AdS higher-spin holographic correspondences [145][146][147][148][149] and our results may pave the way to non-AdS holographic scenarios involving higher-spin fields even in four or more space-time dimensions (see, e.g., [28,29] for an analysis of the symmetries that may be relevant to flat-space higher-spin holography in any dimensions).…”

Supersymmetric localization on dS: sum over topologies

“…With the connection between 3d Euclidean gravity and the supersymmetric CS theory made explicit in Eqs. (8) and 10, we will now evaluate the partition function of the 3d supersymmetric CS theory via supersymmetric Localization techniques. Since, we are interested in evaluating gravity partition function on lens spaces, we would we would try localizing the CS theory on lens spaces L( p, q).…”

“…(38), we refer the reader to [30]. 8 We only draw our reader's attention to the fact that the above expression reduces to the 1-loop determinant of the partition function evaluated on S 3 for the special case of p = 1 and q * = 0 as it should as L(1, 0) = S 3 .…”

“…In this sector, one attempts at quantum gravity for asymptotically flat space-time, now equipped with the BMS 3 algebra. [8] contains a relatively extensive discussion of quantum gravity in 3 dimensions from the perspective of asymptotic symmetries for asymptotically non-AdS spacetime, even including higher spin degrees of freedom.…”

Holographic calculation of BMSFT mutual and 3-partite information

“…Using this duality one can find the universal properties of BMSFTs by merely performing calculations on the gravity side (see [28] for a complete list of related papers). In the rest of this paper we use the above mentioned duality to study the mutual information and 3-partite information of BMSFTs.…”