25 research outputs found
FRW and domain walls in higher spin gravity
We present exact solutions to Vasiliev's bosonic higher spin gravity
equations in four dimensions with positive and negative cosmological constant
that admit an interpretation in terms of domain walls, quasi-instantons and
Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are
infinite dimensional higher-spin extensions of spacetime isometries generated
by six Killing vectors. The solutions presented are obtained by using a method
of holomorphic factorization in noncommutative twistor space and gauge
functions. In interpreting the solutions in terms of Fronsdal-type fields in
spacetime, a field-dependent higher spin transformation is required, which is
implemented at leading order. To this order, the scalar field solves
Klein-Gordon equation with conformal mass in (anti) de Sitter space. We
interpret the FRW solution with de Sitter asymptotics in the context of
inflationary cosmology and we expect that the domain wall and FRW solutions are
associated with spontaneously broken scaling symmetries in their holographic
description. We observe that the factorization method provides a convenient
framework for setting up a perturbation theory around the exact solutions, and
we propose that the nonlinear completion of particle excitations over FRW and
domain wall solutions requires black hole-like states.Comment: 63 page
Supersymmetric Higher Spin Theories
We revisit the higher spin extensions of the anti de Sitter algebra in four
dimensions that incorporate internal symmetries and admit representations that
contain fermions, classified long ago by Konstein and Vasiliev. We construct
the , Euclidean and Kleinian version of these algebras, as well as the
corresponding fully nonlinear Vasiliev type higher spin theories, in which the
reality conditions we impose on the master fields play a crucial role. The
supersymmetric higher spin theory in , on which we elaborate
further, is included in this class of models. A subset of Konstein-Vasiliev
algebras are the higher spin extensions of the superalgebras
for mod 4 and can be realized using
fermionic oscillators. We tensor the higher superalgebras of the latter kind
with appropriate internal symmetry groups and show that the mod 4
higher spin algebras are isomorphic to those with mod 4. We
describe the fully nonlinear higher spin theories based on these algebras as
well, and we elaborate further on the supersymmetric theory,
providing two equivalent descriptions one of which exhibits manifestly its
relation to the supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin
Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie
An action principle for Vasiliev's four-dimensional higher-spin gravity
We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge
fields in four spacetime dimensions with an action principle. We first extend
Vasiliev's original system with differential forms in degrees higher than one.
We then derive the resulting duality-extended equations of motion from a
variational principle based on a generalized Hamiltonian sigma-model action.
The generalized Hamiltonian contains two types of interaction freedoms: One set
of functions that appears in the Q-structure of the generalized curvatures of
the odd forms in the duality-extended system; and another set depending on the
Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of
polyvector fields of ranks two or higher in target space. We find that at least
one of the two sets of interaction-freedom functions must be linear in order to
ensure gauge invariance. We discuss consistent truncations to the minimal Type
A and B models (with only even spins), spectral flows on-shell and provide
boundary conditions on fields and gauge parameters that are compatible with the
variational principle and that make the duality-extended system equivalent, on
shell, to Vasiliev's original system.Comment: 37 pages. References added, corrected typo
Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
We present some generalities of unfolded on-shell dynamics that are useful in
analysing the BMV conjecture for mixed-symmetry fields in constantly curved
backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra
modules generated from primary Weyl tensors of arbitrary mass and shape, and in
backgrounds with general values of the cosmological constant. We also discuss
the unfolded notion of local degrees of freedom in theories with and without
gravity and with and without massive deformation parameters, using the language
of Weyl zero-form modules and their duals.Comment: Corrected typos, references added, two figures, some remarks and two
subsections added for clarit
Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization
Following the general formalism presented in arXiv:0812.3615 -- referred to
as Paper I -- we derive the unfolded equations of motion for tensor fields of
arbitrary shape and mass in constantly curved backgrounds by radial reduction
of Skvortsov's equations in one higher dimension. The complete unfolded system
is embedded into a single master field, valued in a tensorial Schur module
realized equivalently via either bosonic (symmetric basis) or fermionic
(anti-symmetric basis) vector oscillators. At critical masses the reduced Weyl
zero-form modules become indecomposable. We explicitly project the latter onto
the submodules carrying Metsaev's massless representations. The remainder of
the reduced system contains a set of Stueckelberg fields and dynamical
potentials that leads to a smooth flat limit in accordance with the
Brink--Metsaev--Vasiliev (BMV) conjecture. In the unitary massless cases in
AdS, we identify the Alkalaev--Shaynkman--Vasiliev frame-like potentials and
explicitly disentangle their unfolded field equations.Comment: 67 pages, typos corrected, clarifying comments adde
On gravitational interactions for massive higher spins in
In this paper we investigate gravitational interactions of massive higher
spin fields in three dimensional space with arbitrary value of
cosmological constant including flat Minkowski space. We use frame-like gauge
description for such massive fields adopted to three-dimensional case. At
first, we carefully analyze the procedure of switching on gravitational
interactions in the linear approximation on the example of massive spin-3 field
and then proceed with the generalization to the case of arbitrary integer spin
field. As a result we construct a cubic interaction vertex linear in spin-2
field and quadratic in higher spin field on background. As in the
massless case the vertex does not contain any higher derivative corrections to
the Lagrangian and/or gauge transformations. Thus, even after switching on
gravitational interactions, one can freely consider any massless or partially
massless limits as well as the flat one.Comment: 21 pages. Some clarifications and 1 new reference added. Version to
appear in the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT"
edited by Matthias Gaberdiel and Mikhail Vasilie
Propagating modes of non-Abelian tensor gauge field of second rank
In the recently proposed extension of the YM theory, non-Abelian tensor gauge
field of the second rank is represented by a general tensor whose symmetric
part describes the propagation of charged gauge boson of helicity two and its
antisymmetric part - the helicity zero charged gauge boson. On the
non-interacting level these polarizations are similar to the polarizations of
the graviton and of the Abelian antisymmetric B field, but the interaction of
these gauge bosons carrying non-commutative internal charges cannot be directly
identified with the interaction of gravitons or B field. Our intention here is
to illustrate this result from different perspectives which would include
Bianchi identity for the corresponding field strength tensor and the analysis
of the second-order partial differential equation which describes in this
theory the propagation of non-Abelian tensor gauge field of the second rank.Comment: 22 pages, Latex fil
A minimal BV action for Vasiliev's four-dimensional higher spin gravity
The action principle for Vasiliev's four-dimensional higher-spin gravity
proposed recently by two of the authors, is converted into a minimal BV master
action using the AKSZ procedure, which amounts to replacing the classical
differential forms by vectorial superfields of fixed total degree given by the
sum of form degree and ghost number. The nilpotency of the BRST operator is
achieved by imposing boundary conditions and choosing appropriate gauge
transitions between charts leading to a globally-defined formulation based on a
principal bundle.Comment: 39 pages, 1 figure. Additional comments in the conclusion
The Higher Spin/Vector Model Duality
This paper is mainly a review of the dualities between Vasiliev's higher spin
gauge theories in AdS4 and three dimensional large N vector models, with focus
on the holographic calculation of correlation functions of higher spin
currents. We also present some new results in the computation of parity odd
structures in the three point functions in parity violating Vasiliev theories.Comment: 55 pages, 1 figure. Contribution to J. Phys. A special volume on
"Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev.
v2: references adde
Black holes in three dimensional higher spin gravity: A review
We review recent progress in the construction of black holes in three
dimensional higher spin gravity theories. Starting from spin-3 gravity and
working our way toward the theory of an infinite tower of higher spins coupled
to matter, we show how to harness higher spin gauge invariance to consistently
generalize familiar notions of black holes. We review the construction of black
holes with conserved higher spin charges and the computation of their partition
functions to leading asymptotic order. In view of the AdS/CFT correspondence as
applied to certain vector-like conformal field theories with extended conformal
symmetry, we successfully compare to CFT calculations in a generalized Cardy
regime. A brief recollection of pertinent aspects of ordinary gravity is also
given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume
on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M.
Vasilie