Actions for self-dual Higher Spin Gravities

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.

Characteristic cohomology and observables in higher spin gravity

We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

On the spectrum of pure higher spin gravity

We study the spectrum of pure massless higher spin theories in AdS3. The light spectrum is given by a tower of massless particles of spin s = 2, ⋯ , N and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the $$ {\mathcal{W}}_N $$ W N algebra. Modular invariance puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with unitarity. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the central charge. We show that these states can be interpreted as conical defects with deficit angle 2π(1 − 1/M). Unitarity allows the inclusion of such defects into the path integral provided M ≥ N.

Integrable systems and the boundary dynamics of higher spin gravity on AdS3

We introduce a new set of boundary conditions for three-dimensional higher spin gravity with gauge group SL(3, ℝ) × SL(3, ℝ), where its dynamics at the boundary is described by the members of the modified Boussinesq integrable hierarchy. In the asymptotic region the gauge fields are written in the diagonal gauge, where the excitations go along the generators of the Cartan subalgebra of sl(3, ℝ) ⊕ sl(3, ℝ). We show that the entire integrable structure of the modified Boussinesq hierarchy, i.e., the phase space, the Poisson brackets and the infinite number of commuting conserved charges, are obtained from the asymptotic structure of the higher spin theory. Furthermore, its known relation with the Boussinesq hierarchy is inherited from our analysis once the asymptotic conditions are re-expressed in the highest weight gauge. Hence, the Miura map is recovered from a purely geometric construction in the bulk. Black holes that fit within our boundary conditions, the Hamiltonian reduction at the boundary, and the generalization to higher spin gravity with gauge group SL(N, ℝ) × SL(N, ℝ) are also discussed.

Supersymmetric localization on dS: sum over topologies

We find the exact quantum gravity partition function on the static patch of 3d de Sitter spacetime. We have worked in the Chern Simons formulation of 3d gravity. To obtain a non-perturbative result, we supersymmetrized the Chern Simons action and used the technique of supersymmetric localization. We have obtained an exact non-perturbative result for the spin-2 gravity case. We comment on the divergences present in the theory. We also comment on higher spin gravity theories and analyse the nature of divergences present in such theories.