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Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theories. The actions give examples of complete higher spin theories both in flat and (anti)-de Sitter spaces that feature gauge and gravitational interactions. The actions are based on a new description of higher spin fields, whose origin can be traced to early works on twistor theory. The new description simplifies the structure of interactions. In particular, we find a covariant form of the minimal gravitational interaction for higher spin fields both in flat and anti-de Sitter space, which resolves some of the puzzles in the literature.
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In higher derivative theories, gravity can travel slower or faster than light. With this feature in mind, we revisit the construction of the causal and entanglement wedges in this type of theories, and argue that they must be constructed using the fastest mode instead of null rays. We show that the property of causal wedge inclusion, i.e., the fact that the causal wedge must be contained in the entanglement wedge, leads to more stringent constraints on the couplings than those imposed by hyperbolicity and boundary causality. Our results imply that the full power of subregion-subregion duality could lead to the same conclusions previously obtained based on high energy graviton scattering. We illustrate our findings with a systematic analysis in Gauss-Bonnet gravity.
We propose a non-abelian higher-spin theory in two dimensions for an infinite multiplet of massive scalar fields and infinitely many topological higher-spin gauge fields together with their dilaton-like partners. The spectrum includes local degrees of freedom although the field equations take the form of flatness and covariant constancy conditions because fields take values in a suitable extension of the infinite-dimensional higher-spin algebra $hs[lambda]$. The corresponding action functional is of BF-type and generalizes the known topological higher-spin Jackiw-Teitelboim gravity.
We study the problem of interacting theories with (partially)-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends the well-known class of purely massless theories. More generally, it is proved that the complete theory has to have a form of the flatness condition for a connection of a Lie algebra, which, provided there is a non-degenerate invariant bilinear form, can be derived from the Chern-Simons action. We also point out the existence of higher spin theories without the dynamical graviton in the spectrum. As an application of a more general statement that the frame-like formulation can be systematically constructed starting from the metric one by employing a combination of the local BRST cohomology technique and the parent formulation approach, we also obtain an explicit uplift of any given metric-like vertex to its frame-like counterpart. This procedure is valid for general gauge theories while in the case of higher spin fields in d-dimensional Minkowski space one can even use as a starting point metric-like vertices in the transverse-traceless gauge. In particular, this gives the fully off-shell lift for transverse-traceless vertices.
In $d$ dimensions, the model for a massless $p$-form in curved space is known to be a reducible gauge theory for $p>1$, and therefore its covariant quantisation cannot be carried out using the standard Faddeev-Popov scheme. However, adding a mass term and also introducing a Stueckelberg reformulation of the resulting $p$-form model, one ends up with an irreducible gauge theory which can be quantised `a la Faddeev and Popov. We derive a compact expression for the massive $p$-form effective action, $Gamma^{(m)}_p$, in terms of the functional determinants of Hodge-de Rham operators. We then show that the effective actions $Gamma^{(m)}_p$ and $Gamma^{(m)}_{d-p-1}$ differ by a topological invariant. This is a generalisation of the known result in the massless case that the effective actions $Gamma_p$ and $Gamma_{d-p-2}$ coincide modulo a topological term. Finally, our analysis is extended to the case of massive super $p$-forms coupled to background ${cal N}=1$ supergravity in four dimensions. Specifically, we study the quantum dynamics of the following massive super $p$-forms: (i) vector multiplet; (ii) tensor multiplet; and (iii) three-form multiplet. It is demonstrated that the effective actions of the massive vector and tensor multiplets coincide. The effective action of the massive three-form is shown to be a sum of those corresponding to two massive scalar multiplets, modulo a topological term.
The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms together with their duals and is manifestly duality invariant. Space-time covariance is no longer manifest but still present with a non-standard realization of space-time diffeomorphisms on the gauge fields. In this paper, we give a non-abelian generalization of this first-order action by gauging part of its global symmetries. The resulting field equations are non-abeli
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