316 research outputs found
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 as
well as their connection to Weinberg's result. While the procedure we follow
can be shown to be consistent in any , no infinite-dimensional enhancement
of the asymptotic symmetry group emerges from it in , 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 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 CFT's: the generators of the residual
gauge symmetries are the classical limits of screening charges, while the
gauge-invariant observables are classical charges. Quantization in these
variables can be carried out using standard techniques and makes manifest a
remnant of the triality symmetry of . 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
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
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