2 research outputs found
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
Collective Dipole Model of AdS/CFT and Higher Spin Gravity
We formulate a first quantized construction of the AdS_{d+1}/CFT_d
correspondence using the bi-local representation of the free d-dimensional
large N vector model. The earlier reconstruction of AdS_4 higher-spin gravity
provides a scheme where the AdS spacetime (and higher-spin fields) are given by
the composite bi-local fields. The underlying first quantized, world-sheet
picture is extracted in the present work and generalized to any dimension. A
higher-spin AdS particle model is shown to emerge from the collective
bi-particle system of Minkowski particles through a canonical transformation.
As such this construction provides a simple explicit mechanism of the AdS/CFT
correspondence.Comment: 16 pages, no figures; v2: references added; v3: minor change