u-Wigner Contraction Research Articles

Hypersymmetric extensions of Maxwell-Chern-Simons gravity in 2+1 dimensions

We present a consistent way of coupling three-dimensional Maxwell Chern-Simons gravity theory with massless spin-$\frac{5}{2}$ gauge fields. We first introduce the simplest hyper-Maxwell Chern-Simons gravity containing two massless spin-2 fields coupled with a massless Majorana fermion of spin-$\frac{5}{2}$ and whose novel underlying superalgebra is explicitly constructed. Then, we present three alternative hypersymmetric extensions of the Maxwell algebra which are shown to emerge from the In\"on\"u-Wigner contraction procedure of precise combinations of the $\mathfrak{osp}\left(1|4\right)$ and the $\mathfrak{sp}\left(4\right)$ algebras. This allow us to construct distinct types of hyper-Maxwell Chern-Simons theories that extend to include generically interacting non-propagating spin-$4$ fields accompanied by one or two spin-$\frac{5}{2}$ gauge fields.

Cosmology from a gauge induced gravity

The main goal of the present work is to analyze the cosmological scenario of the induced gravity theory developed in previous works. Such a theory consists on a Yang-Mills theory in a four-dimensional Euclidian spacetime with $SO(m,n)$ such that $m+n=5$ and $m\in\{0,1,2\}$ as its gauge group. This theory undergoes a dynamical gauge symmetry breaking via an In\"on\"u-Wigner contraction in its infrared sector. As a consequence, the $SO(m,n)$ algebra is deformed into a Lorentz algebra with the emergency of the local Lorentz symmetries and the gauge fields being identified with a vierbein and a spin connection. As a result, gravity is described as an effective Einstein-Cartan-like theory with ultraviolet correction terms and a propagating torsion field. We show that the cosmological model associated with this effective theory has three different regimes. In particular, the high curvature regime presents a de Sitter phase which tends towards a $\Lambda$CDM model. We argue that $SO(m,n)$ induced gravities are promising effective theories to describe the early phase of the universe.

Infinite S-expansion with ideal subtraction and some applications

According to the literature, the S-expansion procedure involving a finite semigroup is valid no matter what the structure of the original Lie (super)algebra is; however, when something about the structure of the starting (super)algebra is known and when certain particular conditions are met, the S-expansion method (with its features of resonance and reduction) is able not only to lead to several kinds of expanded (super)algebras but also to reproduce the effects of the standard as well as the generalized Inönü-Wigner contraction. In the present paper, we propose a new prescription for S-expansion, involving an infinite abelian semigroup S(∞) and the subtraction of an infinite ideal subalgebra. We show that the subtraction of the infinite ideal subalgebra corresponds to a reduction. Our approach is a generalization of the finite S-expansion procedure presented in the literature, and it offers an alternative view of the generalized Inönü-Wigner contraction. We then show how to write the invariant tensors of the target (super)algebras in terms of those of the starting ones in the infinite S-expansion context presented in this work. We also give some interesting examples of application on algebras and superalgebras.

Chern–Simons and Born–Infeld gravity theories and Maxwell algebras type

Recently was shown that standard odd and even-dimensional General Relativity can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld Lagrangian invariant under a subalgebra $\cal{L}^{B_{2n+1}}$ respectively. Very Recently, it was shown that the generalized In\"on\"u-Wigner contraction of the generalized AdS-Maxwell algebras provides Maxwell algebras types $\cal{M}_{m}$ which correspond to the so called $B_{m}$ Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional General Relativity may emerge as a weak coupling constant limit of a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the Maxwell algebra type $\cal{M}_{2m+1}$, if and only if $m\geq p$. Similarly, we show that standard even-dimensional General Relativity emerges as a weak coupling constant limit of a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under a subalgebra $\cal{L}^{\cal{M}_{2m}}$ of the Maxwell algebra type, if and only if $m\geq p$. It is shown that when $m<p$ this is not possible for a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the $\cal{M}_{2m+1}$ and for a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under $\cal{L}^{\cal{M}_{2m}}$ algebra.

Symmetries of field equations of axion electrodynamics

The group classification of models of axion electrodynamics with arbitrary self-interaction of axionic field is carried out. It is shown that extensions of the basic Poincar\'e invariance of these models appear only for constant and exponential interactions. The related conservation laws are discussed. The maximal continuous symmetries of the 3d Chern-Simons electrodynamics and Carroll-Field-Jackiw electrodynamics are presented. Using the In\"on\"u-Wigner contraction the nonrelativistic limit of equations of axion electrodynamics is found. Exact solutions for the electromagnetic and axion fields are discussed including those which describe propagation with group velocities faster than the speed of light. However these solutions are causal since the corresponding energy velocities are subluminal.

De Sitter gauge theories and induced gravities

Pure de Sitter, anti de Sitter, and orthogonal gauge theories in four-dimensional Euclidean spacetime are studied. It is shown that, if the theory is asymptotically free and a dynamical mass is generated, then an effective geometry may be induced and a gravity theory emerges. The asymptotic freedom and the running of the mass might account for an In\"on\"u-Wigner contraction which induces a breaking of the gauge group to the Lorentz group, while the mass itself is responsible for the coset sector of the gauge field to be identified with the effective vierbein. Furthermore, the resulting local isometries are Lorentzian for the anti de Sitter group and Euclidean for the de Sitter and orthogonal groups.

Scaling limit ofN=6superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories

We show that the $\mathcal{N}=8$ superconformal Bagger-Lambert theory based on the Lorentzian 3-algebra can be derived by taking a certain scaling limit of the recently proposed $\mathcal{N}=6$ superconformal $U(N)\ifmmode\times\else\texttimes\fi{}U(N)$ Chern-Simons-matter theories at level $(k,\ensuremath{-}k)$. The scaling limit (and In\"on\"u-Wigner contraction) is to scale the trace part of the bifundamental fields as ${X}_{0}\ensuremath{\rightarrow}{\ensuremath{\lambda}}^{\ensuremath{-}1}{X}_{0}$ and an axial combination of the two gauge fields as ${B}_{\ensuremath{\mu}}\ensuremath{\rightarrow}\ensuremath{\lambda}{B}_{\ensuremath{\mu}}$. Simultaneously, we scale the level as $k\ensuremath{\rightarrow}{\ensuremath{\lambda}}^{\ensuremath{-}1}k$ and then take $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ limit. Interestingly, the same constraint equation ${\ensuremath{\partial}}^{2}{X}_{0}=0$ is derived by imposing finiteness of the action. In this scaling limit, M2 branes are located far from the origin of ${\mathbf{C}}^{4}/{\mathbf{Z}}_{\mathbf{k}}$ compared to their fluctuations and ${\mathbf{Z}}_{\mathbf{k}}$ identification becomes a circle identification. Hence, the scaled theory describes $\mathcal{N}=8$ supersymmetric theory of 2-branes with dynamical coupling. The coupling constant is promoted to a space-time dependent $SO(8)$ vector ${X}_{0}^{I}$ and we show that the scaled theory has a generalized conformal symmetry as well as manifest $SO(8)$ with the transformation of the background fields ${X}_{0}^{I}$.