471 research outputs found
Higher spin matrix models
We propose a hybrid class of theories for higher spin gravity and matrix
models, i.e. which handle simultaneously higher spin gravity fields and matrix
models. The construction is similar to Vasiliev's higher spin gravity but part
of the equations of motion are provided by the action principle of a matrix
model. In particular we construct a higher spin (gravity) matrix model related
to type IIB matrix models/string theory which have a well defined classical
limit, and which is compatible with higher spin gravity in space. As it
has been suggested that higher spin gravity should be related to string theory
in a high energy (tensionless) regime, and therefore to M-Theory, we expect
that our construction will be useful to explore concrete connections.Comment: 13 pages, 1 table. New references and corrections from referee
reports are included in this version. Current form accepted in Universe
journal for the special issue on Higher Spin Gauge Theorie
Topological self-dual vacua of deformed gauge theories
We propose a deformation principle of gauge theories in three dimensions that
can describe topologically stable self-dual gauge fields, i.e., vacua
configurations that in spite of their masses do not deform the background
geometry and are locally undetected by charged particles. We interpret these
systems as describing boundary degrees of freedom of a self-dual Yang-Mills
field in dimensions with mixed boundary conditions. Some of these fields
correspond to Abrikosov-like vortices with an exponential damping in the
direction penetrating into the bulk. We also propose generalizations of these
ideas to higher dimensions and arbitrary p-form gauge connections.Comment: 18 page
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
Quantization of counterexamples to Dirac's conjecture
Dirac's conjecture, that secondary first-class constraints generate
transformations that do not change the physical system's state, has various
counterexamples. Since no matching gauge conditions can be imposed, the Dirac
bracket cannot be defined, and restricting the phase space first and then
quantizing is an inconsistent procedure. The latter observation has discouraged
the study of systems of this kind more profoundly, while Dirac's conjecture is
assumed generally valid. We point out, however, that secondary first-class
constraints are just initial conditions that do not imply Poisson's bracket
modification, and we carry out the quantization successfully by imposing these
constraints on the initial state of the wave function. We apply the method to
two Dirac's conjecture counterexamples, including Cawley's iconical system.Comment: Minor modifications in version 2, 14 pages, references adde
Pseudoclassical system with gauge and time-reparametrization invariance
We present a pseudoclassical mechanics model which exhibits gauge symmetry
and time-reparametrization invariance. As such, first- and second-class
constraints restrict the phase space, and the Hamiltonian weakly vanishes. We
show that the Dirac conjecture does not hold -- the secondary first-class
constraint is not a symmetry generator -- and only the gauge fixing condition
associated with the primary first-class constraint is needed to remove the
gauge ambiguities. The gauge fixed theory is equivalent to the Fermi harmonic
oscillator extended by a boundary term. We quantize in the deformation
quantization and in the Schrodinger representation approaches and observe that
the boundary term prepares the system in the state of positive energy.Comment: 18 page
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