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J. A. de Azcarraga

Publications and source records attributed to J. A. de Azcarraga.

At least 19 recordsLinked to original sources
arXiv2017

Bosonic D=11 supergravity from a generalized Chern-Simons action

It is shown that the action of the bosonic sector of D=11 supergravity may be obtained by means of a suitable scaling of the originally dimensionless fields of a generalized Chern-Simons action. This follows from the eleven-form CS-potential of the most general linear combination of closed, gauge invariant twelve-forms involving the sp(32)-valued two-form curvatures supplemented by a three-form field. In this construction, the role of the skewsymmetric four-index auxiliary function needed for the first order formulation of $D=11$ supergravity is played by the gauge field associated with the five Lorentz indices generator of the bosonic sp(32) subalgebra of osp(1|32).

hep-th↗
arXiv2015

Two-twistor particle models and free massive higher spin fields

We present D=3 and D=4 models for massive particles moving in a new type of enlarged spacetime, with D-1 additional vector coordinates, which after quantization lead to the towers of massive higher spin (HS) free fields. Two classically equivalent formulations are presented: one with a hybrid spacetime/bispinor geometry and a second described by a free two-twistor dynamics with constraints. After quantization in the D=3 and D=4 cases, the wave functions are given as functions on the SL(2,R) and SL(2,C) group manifolds respectively, and describe arbitrary on-shell momenta and spin degrees of freedom. Finally, the D=6 case and possible supersymmetric extensions are mentioned.

hep-th↗
arXiv2014

Minimal D=4 supergravity from the superMaxwell algebra

We show that the first-order D=4, N=1 pure supergravity lagrangian four-form can be obtained geometrically as a quadratic expression in the curvatures of the Maxwell superalgebra. This is achieved by noticing that the relative coefficient between the two terms of the Lagrangian that makes the action locally supersymmetric also determines trivial field equations for the gauge fields associated with the extra generators of the Maxwell superalgebra. Along the way, a convenient geometric procedure to check the local supersymmetry of a class of lagrangians is developed.

hep-th↗
arXiv2013

k-Leibniz algebras from lower order ones: from Lie triple to Lie l-ple systems

Two types of higher order Lie $\ell$-ple systems are introduced in this paper. They are defined by brackets with $\ell > 3$ arguments satisfying certain conditions, and generalize the well known Lie triple systems. One of the generalizations uses a construction that allows us to associate a $(2n-3)$-Leibniz algebra $\fL$ with a metric $n$-Leibniz algebra $\tilde{\fL}$ by using a $2(n-1)$-linear Kasymov trace form for $\tilde{\fL}$. Some specific types of $k$-Leibniz algebras, relevant in the construction, are introduced as well. Both higher order Lie $\ell$-ple generalizations reduce to the standard Lie triple systems for $\ell=3$.

math-ph↗
arXiv2012

Maxwell symmetries and some applications

The Maxwell algebra is the result of enlarging the Poincaré algebra by six additional tensorial Abelian generators that make the fourmomenta non-commutative. We present a local gauge theory based on the Maxwell algebra with vierbein, spin connection and six additional geometric Abelian gauge fields. We apply this geometric framework to the construction of Maxwell gravity, which is described by the Einstein action plus a generalized cosmological term. We mention a Friedman-Robertson-Walker cosmological approximation to the Maxwell gravity field equations, with two scalar fields obtained from the additional gauge fields. Finally, we outline further developments of the Maxwell symmetries framework.

hep-th↗
arXiv2011

Topics on n-ary algebras

We describe the basic properties of two n-ary algebras, the Generalized Lie Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology relevant for the central extensions and infinitesimal deformations of FAs. It is seen that semisimple FAs do not admit central extensions and, moreover, that they are rigid. This extends the familiar Whitehead's lemma to all $n\geq 2$ FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is no longer required to be fully skewsymmetric one is led to the n-Leibniz (or Loday's) algebra structure. Using that FAs are a particular case of n-Leibniz algebras, those with an anticommutative n-bracket, we study the class of n-Leibniz deformations of simple FAs that retain the skewsymmetry for the first n-1 entires of the n-Leibniz bracket.

math-ph↗
arXiv2011

On a class of n-Leibniz deformations of the simple Filippov algebras

We study the problem of the infinitesimal deformations of all real, simple, finite-dimensional Filippov (or n-Lie) algebras, considered as a class of n-Leibniz algebras characterized by having an n-bracket skewsymmetric in its n-1 first arguments. We prove that all n>3 simple finite-dimensional Filippov algebras are rigid as n-Leibniz algebras of this class. This rigidity also holds for the Leibniz deformations of the semisimple n=2 Filippov (i.e., Lie) algebras. The n=3 simple FAs, however, admit a non-trivial one-parameter infinitesimal 3-Leibniz algebra deformation. We also show that the $n\geq 3$ simple Filippov algebras do not admit non-trivial central extensions as n-Leibniz algebras of the above class.

math-ph↗
arXiv2011

Contractions of Filippov algebras

We introduce in this paper the contractions $\mathfrak{G}_c$ of $n$-Lie (or Filippov) algebras $\mathfrak{G}$ and show that they have a semidirect structure as their $n=2$ Lie algebra counterparts. As an example, we compute the non-trivial contractions of the simple $A_{n+1}$ Filippov algebras. By using the İnönü-Wigner and the generalized Weimar-Woods contractions of ordinary Lie algebras, we compare (in the $\mathfrak{G}=A_{n+1}$ simple case) the Lie algebras Lie$\,\mathfrak{G}_c$ (the Lie algebra of inner endomorphisms of $\mathfrak{G}_c$) with certain contractions $(\mathrm{Lie}\,\mathfrak{G})_{IW}$ and $(\mathrm{Lie}\,\mathfrak{G})_{W-W}$ of the Lie algebra Lie$\,\mathfrak{G}$ associated with $\mathfrak{G}$.

math-ph↗
arXiv2009

Galilean Superconformal Symmetries

We consider the non-relativistic c -> \infty contraction limit of the (N=2k)- extended D=4 superconformal algebra su(2,2;N), introducing in this way the non-relativistic (N=2k)-extended Galilean superconformal algebra. Such a Galilean superconformal algebra has the same number of generators as su(2,2|2k). The usp(2k) algebra describes the non-relativistic internal symmetries, and the generators from the coset u(2k)/usp(2k) become central charges after contraction.

math-ph↗
arXiv2009

Supertwistors, massive superparticles and k-symmetry

We consider a D=4 two-twistor lagrangian for a massive particle that incorporates the mass-shell condition in an algebraic way, and extend it to a two-supertwistor model with N=2 supersymmetry and central charge identified with the mass. In the purely supertwistorial picture the two D=4 supertwistors are coupled through a Wess-Zumino term in their fermionic sector. We demonstrate how the kappa-gauge symmetry appears in the purely supertwistorial formulation and reduces by half the fermionic degrees of freedom of the two supertwistors; a formulation of the model in terms of kappa-invariant degrees of freedom is also obtained. We show that the kappa-invariant supertwistor coordinates can be obtained by dimensional (D=6 -> D=4) reduction from a D=6 supertwistor. We derive as well by 6 -> 4 reduction the N=2, D=4 massive superparticle model with Wess-Zumino term introduced in 1982. Finally, we comment on general superparticle models constructed with more than two supertwistors.

hep-th↗
arXiv2007

Expansions of algebras and superalgebras and some applications

After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the Inonu-Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32).

hep-th↗
arXiv2007

BPS preons in M-theory and supergravity

After introducing the notion of BPS preons as the basic constituents of M-theory, we discuss the recent negative results in the search for solutions of the D=10 and D=11 supergravity equations preserving 31/32 supersymmetries i.e., of preonic solutions. The absence of these supergravity preonic solutions may point out to a pure quantum nature of BPS preons, manifesting itself in the need of incorporating quantum (stringy/M-theoretic) corrections to the supergravity equations.

hep-th↗
arXiv2005

Dynamics of Higher Spin Fields and Tensorial Space

The structure and the dynamics of massless higher spin fields in various dimensions are reviewed with an emphasis on conformally invariant higher spin fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal higher spin fields constitute the quantum spectrum of a twistor-like particle propagating in tensorial spaces of corresponding dimensions. We give a detailed analysis of the field equations of the model and establish their relation with known formulations of free higher spin field theory.

hep-th↗
arXiv2005

Generalized curvature and the equations of D=11 supergravity

It is known that, for zero fermionic sector, the bosonic equations of Cremmer-Julia-Scherk eleven-dimensional supergravity can be collected in a compact expression which is a condition on the curvature of the generalized connection. Here we peresent the equation which collects all the bosonic equations of D=11 supergravity when the gravitino is nonvanishing.

hep-th↗
arXiv2004

On BPS preons, generalized holonomies and D=11 supergravities

We develop the BPS preon conjecture to analyze the supersymmetric solutions of D=11 supergravity. By relating the notions of Killing spinors and BPS preons, we develop a moving G-frame method (G=GL(32,R), SL(32,R) or Sp(32,R)) to analyze their associated generalized holonomies. As a first application we derive here the equations determining the generalized holonomies of k/32 supersymmetric solutions and, in particular, those solving the necessary conditions for the existence of BPS preonic (31/32) solutions of the standard D=11 supergravity. We also show that there exist elementary preonic solutions, i.e. solutions preserving 31 out of 32 supersymmetries in a Chern--Simons type supergravity. We present as well a family of worldvolume actions describing the motion of pointlike and extended BPS preons in the background of a D'Auria-Fre type OSp(1|32)-related supergravity model. We discuss the possible implications for M-theory.

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