On Tensorial Spaces and BCFW Recursion Relations for Higher Spin Fields

In this short review we briefly consider two topics in the higher spin gauge theory: the method of "tensorial (super) spaces" and application of BCFW recursion relations to higher spin fields.Comment: 26 pages, Invited Review, discussion improved, references adde

BMS Modules in Three Dimensions

We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an ultrarelativistic limit of highest-weight representations of Virasoro and W algebras, which is to be contrasted with non-relativistic limits that typically give non-unitary representations. To support this dichotomy, we also point out that the ultrarelativistic and non-relativistic limits of generic W algebras differ in the structure of their non-linear terms.Comment: 27 pages; contribution to the proceedings of the workshop "Higher Spin Gauge Theories", Institute for Advanced Studies, NTU, Singapore, November 4-6, 201

New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators

We consider correlation functions of the stress-tensor or a conserved current in AdS_{d+1}/CFT_d computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree level. These relations have an advantage over the BCFW-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including d=3. We also introduce a new method of extracting flat-space S-matrix elements from AdS/CFT correlators in momentum space. We show that the (d+1)-dimensional flat-space amplitude of gravitons or gluons can be obtained as the coefficient of a particular singularity of the d-dimensional correlator of the stress-tensor or a conserved current; this technique is valid even at loop-level in the bulk. Finally, we show that our recursion relations automatically generate correlators that are consistent with this observation: they have the expected singularity and the flat-space gluon or graviton amplitude appears as its coefficient.Comment: 22+6 pages (v2) typos fixe

Asymptotic symmetries and charges at null infinity: from low to high spins

Weinberg's celebrated factorisation theorem holds for soft quanta of arbitrary integer spin. The same result, for spin one and two, has been rederived assuming that the infinite-dimensional asymptotic symmetry group of Maxwell's equations and of asymptotically flat spaces leave the S-matrix invariant. For higher spins, on the other hand, no such infinite-dimensional asymptotic symmetries were known and, correspondingly, no a priori derivation of Weinberg's theorem could be conjectured. In this contribution we review the identification of higher-spin supertranslations and superrotations in $D=4$ as well as their connection to Weinberg's result. While the procedure we follow can be shown to be consistent in any $D$, no infinite-dimensional enhancement of the asymptotic symmetry group emerges from it in $D>4$, thus leaving a number of questions unanswered.Comment: 11 pages. Contribution to the proceedings of Quarks-2018, XXth International Seminar on High Energy Physics; Valday, Russia, 27 May - 2 June 201

Rotating Higher Spin Partition Functions and Extended BMS Symmetries

We evaluate one-loop partition functions of higher-spin fields in thermal flat space with angular potentials; this computation is performed in arbitrary space-time dimension, and the result is a simple combination of Poincar\'e characters. We then focus on dimension three, showing that suitable products of one-loop partition functions coincide with vacuum characters of higher-spin asymptotic symmetry algebras at null infinity. These are extensions of the bms_3 algebra that emerges in pure gravity, and we propose a way to build their unitary representations and to compute the associated characters. We also extend our investigations to supergravity and to a class of gauge theories involving higher-spin fermionic fields.Comment: 58 pages; clarifications and references added; version to be published in JHE

Quantizing higher-spin gravity in free-field variables

We study the formulation of massless higher-spin gravity on AdS$_3$ in a gauge in which the fundamental variables satisfy free field Poisson brackets. This gauge choice leaves a small portion of the gauge freedom unfixed, which should be further quotiented out. We show that doing so leads to a bulk version of the Coulomb gas formalism for $W_N$ CFT's: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical $W_N$ charges. Quantization in these variables can be carried out using standard techniques and makes manifest a remnant of the triality symmetry of $W_\infty[\lambda]$. This symmetry can be used to argue that the theory should be supplemented with additional matter content which is precisely that of the Prokushkin-Vasiliev theory. As a further application, we use our formulation to quantize a class of conical surplus solutions and confirm the conjecture that these are dual to specific degenerate $W_N$ primaries, to all orders in the large central charge expansion.Comment: 31 pages + appendices. V2: typos corrected, reference adde

The action for higher spin black holes in three dimensions

In the context of (2+1)--dimensional Chern-Simons SL(N,R)\times SL(N,R) gauge fields and spin N black holes we compute the on-shell action and show that it generates sensible and consistent thermodynamics. In particular, the Chern-Simons action solves the integrability conditions recently considered in the literature.Comment: Paper shortened and generalized. Main results unchanged. 25 pages, Latex, no figure

On the relation between local and geometric Lagrangians for higher spins

Equations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition, either contain higher derivatives or involve inverse powers of the d'Alembertian operator, thus introducing possible subtleties in degrees of freedom count. We suggest a path to avoid ambiguities, starting from local, unconstrained Lagrangians previously proposed, and integrating out the auxiliary fields from the functional integral, thus generating a unique non-local theory expressed in terms of curvatures.Comment: 14 pages. Contribution to the proceedings of the 1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbary (Crete, Greece) September 14-18 200

An AdS_3 Dual for Minimal Model CFTs

We propose a duality between the 2d W_N minimal models in the large N 't Hooft limit, and a family of higher spin theories on AdS_3. The 2d CFTs can be described as WZW coset models, and include, for N=2, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the RG flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an AdS_4 dual for the singlet sector of large N vector models.Comment: 33 pages LaTe

Triality in Minimal Model Holography

The non-linear W_{\infty}[\mu] symmetry algebra underlies the duality between the W_N minimal model CFTs and the hs[\mu] higher spin theory on AdS_3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a`triality') between three (generically) distinct values of the parameter \mu. This explains, among other things, the agreement of symmetries between the W_N minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest W_{\infty}[\mu] representations, thereby clarifying the analytic continuation between the`light states' of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.Comment: 29 pages; v2. Typos correcte