6 research outputs found
Minimal Model Holography
We review the duality relating 2d W_N minimal model CFTs, in a large N 't
Hooft like limit, to higher spin gravitational theories on AdS_3.Comment: 54 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. minor change
Second-Order Formalism for 3D Spin-3 Gravity
A second-order formalism for the theory of 3D spin-3 gravity is considered.
Such a formalism is obtained by solving the torsion-free condition for the spin
connection \omega^a_{\mu}, and substituting the result into the action
integral. In the first-order formalism of the spin-3 gravity defined in terms
of SL(3,R) X SL(3,R) Chern-Simons (CS) theory, however, the generalized
torsion-free condition cannot be easily solved for the spin connection, because
the vielbein e^a_{\mu} itself is not invertible. To circumvent this problem,
extra vielbein-like fields e^a_{\mu\nu} are introduced as a functional of
e^a_{\mu}. New set of affine-like connections \Gamma_{\mu M}^N are defined in
terms of the metric-like fields, and a generalization of the Riemann curvature
tensor is also presented. In terms of this generalized Riemann tensor the
action integral in the second-order formalism is expressed. The transformation
rules of the metric and the spin-3 gauge field under the generalized
diffeomorphims are obtained explicitly. As in Einstein gravity, the new
affine-like connections are related to the spin connection by a certain gauge
transformation, and a gravitational CS term expressed in terms of the new
connections is also presented.Comment: 40 pages, no figures. v2:references added, coefficients of eqs in
apppendix D corrected, minor typos also corrected, v3:Version accepted for
publication in Classical and Quantum Gravit
Holography, Unfolding and Higher-Spin Theory
Holographic duality is argued to relate classes of models that have
equivalent unfolded formulation, hence exhibiting different space-time
visualizations for the same theory. This general phenomenon is illustrated by
the higher-spin gauge theory shown to be dual to the theory of 3d
conformal currents of all spins interacting with 3d conformal higher-spin
fields of Chern-Simons type. Generally, the resulting 3d boundary conformal
theory is nonlinear, providing an interacting version of the 3d boundary sigma
model conjectured by Klebanov and Polyakov to be dual to the HS theory
in the large limit. Being a gauge theory it escapes the conditions of the
theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory
to be free. Two reductions of particular higher-spin gauge theories where
boundary higher-spin gauge fields decouple from the currents and which have
free boundary duals are identified. Higher-spin holographic duality is also
discussed for the cases of and duality between higher-spin
theories and nonrelativistic quantum mechanics. In the latter case it is shown
in particular that () geometry in the higher-spin setup is dual to
the (inverted) harmonic potential in the quantum-mechanical setup.Comment: 57 pages, V2: Acknowledgements, references, comments, clarifications
and new section on reductions of particular HS theories associated with free
boundary theories are added. Typos corrected, V3. Minor corrections:
clarification in section 9 is added and typos correcte
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