arXiv subjects

Mauricio Valenzuela

Publications and source records attributed to Mauricio Valenzuela.

30 records · Page 2Linked to original sources

arXiv2016

Action principles for higher and fractional spin gravities

We review various off-shell formulations for interacting higher-spin systems in dimensions 3 and 4. Associated with higher-spin systems in spacetime dimension 4 is a Chern-Simons action for a superconnection taking its values in a direct product of an infinite-dimensional algebra of oscillators and a Frobenius algebra. A crucial ingredient of the model is that it elevates the rigid closed and central two-form of Vasiliev's theory to a dynamical 2-form and doubles the higher-spin algebra, thereby considerably reducing the number of possible higher spin invariants and giving a nonzero effective functional on-shell. The two action principles we give for higher-spin systems in 3D are based on Chern-Simons and BF models. In the first case, the theory we give unifies higher-spin gauge fields with fractional-spin fields and an internal sector. In particular, Newton's constant is related to the coupling constant of the internal sector. In the second case, the BF action we review gives the fully nonlinear Prokushkin-Vasiliev, bosonic equations for matter-coupled higher spins in 3D. We present the truncation to a single, real matter field relevant in the Gaberdiel-Gopakumar holographic duality. The link between the various actions we present is the fact that they all borrow ingredients from Topological Field Theory. It has bee conjectured that there is an underlying and unifying 2-dimensional first-quantised description of the previous higher-spin models in 3D and 4D, in the form of a Cattaneo-Felder-like topological action containing fermionic fields.

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arXiv2016

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.

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arXiv2014

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.

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arXiv2014

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.

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arXiv2013

A Higher-Spin Chern-Simons Theory of Anyons

We propose Chern-Simons models of fractional-spin fields interacting with ordinary tensorial higher-spin fields and internal color gauge fields. For integer and half-integer values of the fractional spins, the model reduces to finite sets of fields modulo infinite-dimensional ideals. We present the model on-shell using Fock-space representations of the underlying deformed-oscillator algebra.

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arXiv2012

Supersymmetry of a different kind

A local supersymmetric action for a (2+1)-dimensional system including gravity, the electromagnetic field and a Dirac spin-1/2 field is presented. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields enter as parts of the connection, that transforms in the adjoint representation of the gauge group. The system is off-shell invariant under local (gauge) supersymmetry. Although the supersymmetry is locally realized, there is no spin-3/2 gravitino, and is therefore not supergravity. The fields do not necessarily form supersymmetric doublets of equal mass, and moreover, the fermion may acquire mass through the coupling with the background geometry, while the bosons --the U(1) field and the spin connection-- remain massless.

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arXiv2010

Supersymmetry of the planar Dirac - Deser-Jackiw-Templeton system, and of its non-relativistic limit

The planar Dirac and the topologically massive vector gauge fields are unified into a supermultiplet involving no auxiliary fields. The superPoincaré symmetry emerges from the $osp(1|2)$ supersymmetry realized in terms of the deformed Heisenberg algebra underlying the construction. The non-relativistic limit yields spin 1/2 as well as new, spin 1 "Lévy-Leblond-type" equations which, together, carry an N=2 superSchrödinger symmetry. Part of the latter has its origin in the universal enveloping algebra of the superPoincaré algebra.

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arXiv2010

Bosons, fermions and anyons in the plane, and supersymmetry

Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2+1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N=1 and N=2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Levy-Leblond's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, "Jackiw-Nair" limit (that corresponds to Inonu-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and the supersymmetric cases.

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arXiv2010

Supersymmetry between Jackiw-Nair and Dirac-Majorana anyons

The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N=1 supermultiplet, which carries a super-Poincare symmetry.

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arXiv2009

An infinite supermultiplet of massive higher-spin fields

The representation theory underlying the infinite-component relativistic wave equation written by Majorana is revisited from a modern perspective. On the one hand, the massless solutions of this equation are shown to form a supermultiplet of the superPoincare algebra with tensorial central charges; it can also be obtained as the infinite spin limit of massive solutions. On the other hand, the Majorana equation is generalized for any space-time dimension and for arbitrary Regge trajectories. Inspired from these results, an infinite supermultiplet of massive fields of all spins and of equal mass is constructed in four dimensions and proved to carry an irreducible representation of the orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial charges.

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arXiv2007

Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields

We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin deegres of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.

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arXiv2007

Bosonized supersymmetry of anyons and supersymmetric exotic particle on the non-commutative plane

A covariant set of linear differential field equations, describing an N=1 supersymmetric anyon system in (2+1)D, is proposed in terms of Wigner's deformation of the bosonic Heisenberg algebra. The non-relativistic ``Jackiw-Nair'' limit extracts the ordinary bosonic and fermionic degrees of freedom from the Heisenberg-Wigner algebra. It yields first-order, non-relativistic wave equations for a spinning particle on the non-commutative plane that admits a Galilean exotic planar N=1 supersymmetry.

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