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 $AdS$ 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 $2+2$ 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 $gl(2l+1)$ or $gl(l|l+1)$ 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