155 research outputs found
A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
In Vasiliev's unfolded formulation of higher-spin dynamics the standard
fields are embedded on-shell into covariantly constant master fields valued in
Lorentz-covariant slices of the star-product algebra A of functions on the
singleton phase space. Correspondingly, the harmonic expansion is taken over
compact slices of A that are unitarizable in a rescaled trace-norm rather than
the standard Killing norm. Motivated by the higher-derivative nature of the
theory, we examine indecomposable unitarizable Harish-Chandra modules
consisting of standard massless particles plus linearized runaway solutions.
This extension arises naturally in the above fiber approach upon realizing
compact-weight states as non-polynomial analytic functions in A.Comment: 80 pages, 2 figures. Minor changes: typos corrected, two footnotes
and references added. To be published in JHE
4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
We construct an infinite-dimensional space of solutions to Vasiliev's
equations in four dimensions that are asymptotic to AdS spacetime and superpose
massless scalar particle modes over static higher spin black holes. Each
solution is obtained by a large gauge transformation of an all-order
perturbatively defined particular solution given in a simple gauge, in which
the spacetime connection vanishes, the twistor space connection is holomorphic,
and all local degrees of freedom are encoded into the residual twistor space
dependence of the spacetime zero-forms. The latter are expanded over two dual
spaces of Fock space operators, corresponding to scalar particle and static
black hole modes, equipped with positive definite sesquilinear and bilinear
forms, respectively. Switching on an AdS vacuum gauge function, the twistor
space connection becomes analytic at generic spacetime points, which makes it
possible to reach Vasiliev's gauge, in which Fronsdal fields arise
asymptotically, by another large transformation given here at first order. The
particle and black hole modes are related by a twistor space Fourier transform,
resulting in a black hole backreaction already at the second order of classical
perturbation theory. We speculate on the existence of a fine-tuned branch of
moduli space that is free from black hole modes and directly related to the
quasi-local deformed Fronsdal theory. Finally, we comment on a possible
interpretation of the higher spin black hole solutions as black-hole
microstates.Comment: 63 pages + appendices; v2: reference added; v3: comments and
references added, typos correcte
Higher Spin Gravity Amplitudes From Zero-form Charges
We examine zero-form charges in Vasiliev's four-dimensional bosonic higher
spin gravities. These are classical observables given by integrals over
noncommutative twistor space of adjoint combinations of the zero-form master
fields, including insertions of delta functions in the deformed oscillators
serving as gauge invariant regulators. The regularized charges admit
perturbative expansions in terms of multi-linear functionals in the Weyl
zero-form, which are Bose symmetric and higher spin invariant by construction,
and that can be interpreted as basic building blocks for higher spin gravity
amplitudes. We compute two- and three-point functions by attaching external
legs given by unfolded bulk-to-boundary propagators, and identify the result
with the two- and three-current correlation functions in theories of free
conformal scalars and fermions in three dimensions. Modulo assumptions on the
structure of the sub-leading corrections, and relying on the generalized
Hamiltonian off-shell formulation, we are thus led to propose an expression for
the free energy as a sum of suitably normalized zero-form chargesComment: V2: Typos corrected, references added, footnote and note added,
discussion section improve
Three-dimensional fractional-spin gravity
Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern--Simons
models consisting of fractional-spin fields coupled to higher-spin gravity and
internal non-abelian gauge fields. The gauge algebras consist of
Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal
algebras intertwined by infinite-dimensional generators in lowest-weight
representations of the Lorentz algebra with fractional spin. In integer or
half-integer non-unitary cases, there exist truncations to gl(N,N +/- 1) or
gl(N|N +/- 1) models. In all non-unitary cases, the internal gauge fields can
be set to zero. At the semi-classical level, the fractional-spin fields are
either Grassmann even or odd. The action requires the enveloping-algebra
representation of the deformed oscillators, while their Fock-space
representation suffices on-shell.Comment: 38 pages, 2 tables. References [7,13,61] added with comments in the
second version. To appear in JHE
Gravitational and gauge couplings in Chern-Simons fractional spin gravity
We provide a necessary and sufficient condition for the consistency of the
supertrace, through the existence of a certain ground state projector. We build
this projector and check its properties to the first two orders in the number
operator and to all orders in the deformation parameter. We then find the
relation between the gravitational and internal gauge couplings in the
resulting unified three-dimensional Chern--Simons theory for Blencowe--Vasiliev
higher spin gravity coupled to fractional spin fields and internal gauge
potentials. We also examine the model for integer or half-integer fractional
spins, where infinite dimensional ideals arise and decouple, leaving finite
dimensional gauge algebras or and various real forms
thereof.Comment: Published in JHEP. 32 pages, 3 figure
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