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de Azcarraga, J. A., Gutiez, D., & Izquierdo, J. M. (2019). Extended D=3 Bargmann supergravity from a Lie algebra expansion. Nucl. Phys. B, 946, 114706–14pp.
Abstract: In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from D = 3, N = 2 superPoincare and its corresponding Chern-Simons supergravity. (C) 2019 The Author(s). Published by Elsevier B.V.
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de Azcarraga, J. A., Fedoruk, S., Izquierdo, J. M., & Lukierski, J. (2015). Two-twistor particle models and free massive higher spin fields. J. High Energy Phys., 04(4), 010–39pp.
Abstract: We present D = 3 and D = 4 world-line models for massive particles moving in a new type of enlarged spacetime, with D-1 additional vector coordinates, which after quantization lead to towers of massive higher spin (HS) free fields. Two classically equivalent formulations are presented: one with a hybrid spacetime/bispinor variables and a second described by a free two-twistor dynamics with constraints. After first quantization in the D = 3 and D = 4 cases, the wave functions satisfying a massive version of Vasiliev's free unfolded equations are given as functions on the SL(2, R) and SL(2, C) group manifolds respectively, which describe arbitrary on-shell momenta and spin degrees of freedom. Further we comment on the D = 6 case, and possible supersymmetric extensions are mentioned as well. Finally, the description of interactions and the Ads/crr duality are briefly considered for massive IHS fields.
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de Azcarraga, J. A., Kamimura, K., & Lukierski, J. (2011). Generalized cosmological term from Maxwell symmetries. Phys. Rev. D, 83(12), 124036–8pp.
Abstract: By gauging the Maxwell spacetime algebra, the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six four-vector fields A(mu)(ab)(x) associated with the six Abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the A(mu)(ab)(x) fields.
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de Azcarraga, J. A., & Izquierdo, J. M. (2010). n-ary algebras: a review with applications. J. Phys. A, 43(29), 293001–117pp.
Abstract: This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations ( it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A(4) model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization.
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