304 research outputs found
Higher Spins in AdS and Twistorial Holography
In this paper we simplify and extend previous work on three-point functions
in Vasiliev's higher spin gauge theory in AdS4. We work in a gauge in which the
space-time dependence of Vasiliev's master fields is gauged away completely,
leaving only the internal twistor-like variables. The correlation functions of
boundary operators can be easily computed in this gauge. We find complete
agreement of the tree level three point functions of higher spin currents in
Vasiliev's theory with the conjectured dual free O(N) vector theory.Comment: 23 pages. v3: minor errors fixed, added comments and reference
Minimal Model Holography for SO(2N)
A duality between the large N 't Hooft limit of the WD_N minimal model CFTs
and a higher spin gravity theory on AdS3 is proposed. The gravity theory has
massless spin fields of all even spins s=2,4,6,..., as well as two real scalar
fields whose mass is determined by the 't Hooft parameter of the CFT. We show
that, to leading order in the large N limit, the 1-loop partition function of
the higher spin theory matches precisely with the CFT partition function.Comment: 21 pages, LaTe
Higher Spin Gauge Theory and Holography: The Three-Point Functions
In this paper we calculate the tree level three-point functions of Vasiliev's
higher spin gauge theory in AdS4 and find agreement with the correlators of the
free field theory of N massless scalars in three dimensions in the O(N) singlet
sector. This provides substantial evidence that Vasiliev theory is dual to the
free field theory, thus verifying a conjecture of Klebanov and Polyakov. We
also find agreement with the critical O(N) vector model, when the bulk scalar
field is subject to the alternative boundary condition such that its dual
operator has classical dimension 2.Comment: 90 pages, 5 figures; v4, minor changes in the introductio
On Classical Solutions of 4d Supersymmetric Higher Spin Theory
We present a simple construction of solutions to the supersymmetric higher
spin theory based on solutions to bosonic theories. We illustrate this for the
case of the Didenko-Vasiliev solution in arXiv:0906.3898, for which we have
found a striking simplification where the higher-spin connection takes the
vacuum value. Studying these solutions further, we check under which conditions
they preserve some supersymmetry in the bulk, and when they are compatible with
the boundary conditions conjectured to be dual to certain 3d SUSY
Chern-Simons-matter theories. We perform the analysis for a variety of theories
with = 2, = 3, = 4 and
= 6 and find a rich spectrum of , and -BPS solutions.Comment: v2: 42 pages, section 5 extended, reference added. Version to appear
in JHE
Effective action in a higher-spin background
We consider a free massless scalar field coupled to an infinite tower of
background higher-spin gauge fields via minimal coupling to the traceless
conserved currents. The set of Abelian gauge transformations is deformed to the
non-Abelian group of unitary operators acting on the scalar field. The gauge
invariant effective action is computed perturbatively in the external fields.
The structure of the various (divergent or finite) terms is determined. In
particular, the quadratic part of the logarithmically divergent (or of the
finite) term is expressed in terms of curvatures and related to conformal
higher-spin gravity. The generalized higher-spin Weyl anomalies are also
determined. The relation with the theory of interacting higher-spin gauge
fields on anti de Sitter spacetime via the holographic correspondence is
discussed.Comment: 40 pages, Some errors and typos corrected, Version published in JHE
Quantum W-symmetry in AdS_3
It has recently been argued that, classically, massless higher spin theories
in AdS_3 have an enlarged W_N-symmetry as the algebra of asymptotic isometries.
In this note we provide evidence that this symmetry is realised
(perturbatively) in the quantum theory. We perform a one loop computation of
the fluctuations for a massless spin field around a thermal AdS_3
background. The resulting determinants are evaluated using the heat kernel
techniques of arXiv:0911.5085. The answer factorises holomorphically, and the
contributions from the various spin fields organise themselves into vacuum
characters of the W_N symmetry. For the case of the hs(1,1) theory consisting
of an infinite tower of massless higher spin particles, the resulting answer
can be simply expressed in terms of (two copies of) the MacMahon function.Comment: 23 pages; v2: References adde
Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
We discuss how to systematically compute the asymptotic symmetry algebras of
generic three-dimensional bosonic higher-spin gauge theories in backgrounds
that are asymptotically AdS. We apply these techniques to a one-parameter
family of higher-spin gauge theories that can be considered as large N limits
of SL(N) x SL(N) Chern-Simons theories, and we provide a closed formula for the
structure constants of the resulting infinite-dimensional non-linear
W-algebras. Along the way we provide a closed formula for the structure
constants of all classical W_N algebras. In both examples the higher-spin
generators of the W-algebras are Virasoro primaries. We eventually discuss how
to relate our basis to a non-primary quadratic basis that was previously
discussed in literature.Comment: 61 page
Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
We consider the conformal field theory of N complex massless scalars in 2+1
dimensions, coupled to a U(N) Chern-Simons theory at level k. This theory has a
't Hooft large N limit, keeping fixed \lambda = N/k. We compute some
correlation functions in this theory exactly as a function of \lambda, in the
large N (planar) limit. We show that the results match with the general
predictions of Maldacena and Zhiboedov for the correlators of theories that
have high-spin symmetries in the large N limit. It has been suggested in the
past that this theory is dual (in the large N limit) to the Legendre transform
of the theory of fermions coupled to a Chern-Simons gauge field, and our
results allow us to find the precise mapping between the two theories. We find
that in the large N limit the theory of N scalars coupled to a U(N)_k
Chern-Simons theory is equivalent to the Legendre transform of the theory of k
fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization
of the latter theory. We conjecture that perhaps this duality is valid also for
finite values of N and k, where on the fermionic side we should now have (for
N_f flavors) a U(k)_{N-N_f/2} theory. Similar results hold for real scalars
(fermions) coupled to the O(N)_k Chern-Simons theory.Comment: 49 pages, 16 figures. v2: added reference
Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions
Cubic couplings between a complex scalar field and a tower of symmetric
tensor gauge fields of all ranks are investigated on any constant curvature
spacetime of dimension d>2. Following Noether's method, the gauge fields
interact with the scalar field via minimal coupling to the conserved currents.
A symmetric conserved current, bilinear in the scalar field and containing up
to r derivatives, is obtained for any rank r from its flat spacetime
counterpart in dimension d+1, via a radial dimensional reduction valid
precisely for the mass-square domain of unitarity in (anti) de Sitter spacetime
of dimension d. The infinite collection of conserved currents and cubic
vertices are summarized in a compact form by making use of generating functions
and of the Weyl/Wigner quantization on constant curvature spaces.Comment: 35+1 pages, v2: two references added, typos corrected, enlarged
discussions in Subsection 5.2 and in Conclusion, to appear in JHE
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