65 research outputs found
Metric- and frame-like higher-spin gauge theories in three dimensions
We study the relation between the frame-like and metric-like formulation of
higher-spin gauge theories in three space-time dimensions. We concentrate on
the theory that is described by an SL(3) x SL(3) Chern-Simons theory in the
frame-like formulation. The metric-like theory is obtained by eliminating the
generalised spin connection by its equation of motion, and by expressing
everything in terms of the metric and a spin-3 Fronsdal field. We give an exact
map between fields and gauge parameters in both formulations. To work out the
gauge transformations explicitly in terms of metric-like variables, we have to
make a perturbative expansion in the spin-3 field. We describe an algorithm how
to do this systematically, and we work out the gauge transformations to cubic
order in the spin-3 field. We use these results to determine the gauge algebra
to this order, and explain why the commutator of two spin-3 transformations
only closes on-shell.Comment: 26 pages, no figure
The large level limit of Kazama-Suzuki models
Limits of families of conformal field theories are of interest in the context
of AdS/CFT dualities. We explore here the large level limit of the
two-dimensional N=(2,2) superconformal W_{n+1} minimal models that appear in
the context of the supersymmetric higher-spin AdS3/CFT2 duality. These models
are constructed as Kazama-Suzuki coset models of the form SU(n+1)/U(n). We
determine a family of boundary conditions in the limit theories, and use the
modular bootstrap to obtain the full bulk spectrum of N=2 super-W_{n+1}
primaries in the theory. We also confirm the identification of this limit
theory as the continuous orbifold C^n/U(n) that was discussed recently.Comment: 20 page
Towards metric-like higher-spin gauge theories in three dimensions
We consider the coupling of a symmetric spin-3 gauge field to
three-dimensional gravity in a second order metric-like formulation. The action
that corresponds to an SL(3,R) x SL(3,R) Chern-Simons theory in the frame-like
formulation is identified to quadratic order in the spin-3 field. We apply our
result to compute corrections to the area law for higher-spin black holes using
Wald's entropy formula.Comment: 29 pages; v2: typos correcte
Vertex-Constraints in 3D Higher Spin Theories
We analyse the constraints imposed by gauge invariance on higher-order
interactions between massless bosonic fields in three-dimensional higher-spin
gravities. We show that vertices of quartic and higher order that are
independent of the cubic ones can only involve scalars and Maxwell fields. As a
consequence, the full non-linear interactions of massless higher-spin fields
are completely fixed by the cubic vertex.Comment: 5 page
The Lorentz Anomaly via Operator Product Expansion
The emergence of a critical dimension is one of the most striking features of
string theory. One way to obtain it is by demanding closure of the Lorentz
algebra in the light-cone gauge quantisation, as discovered for bosonic strings
more than fourty years ago. We give a detailed derivation of this classical
result based on the operator product expansion on the Lorentzian world-sheet
Branes on Group Manifolds, Gluon Condensates, and twisted K-theory
In this work we study the dynamics of branes on group manifolds G deep in the
stringy regime. After giving a brief overview of the various branes that can be
constructed within the boundary conformal field theory approach, we analyze in
detail the condensation processes that occur on stacks of such branes. At large
volume our discussion is based on certain effective gauge theories on
non-commutative `fuzzy' spaces. Using the `absorption of the boundary
spin'-principle which was formulated by Affleck and Ludwig in their work on the
Kondo model, we extrapolate the brane dynamics into the stringy regime. For
supersymmetric theories, the resulting condensation processes turn out to be
consistent with the existence of certain conserved charges taking values in
some non-trivial discrete abelian groups. We obtain strong constraints on these
charge groups for G = SU(N). The results may be compared with a recent proposal
of Bouwknegt and Mathai according to which charge groups on curved spaces X
(with a non-vanishing NSNS 3-form field strength H) are given by the twisted
K-groups K*_H(X).Comment: 33 pages, 1 figur
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