23 research outputs found
Bianchi spaces and their 3-dimensional isometries as S-expansions of 2-dimensional isometries
In this paper we show that some 3-dimensional isometry algebras, specifically
those of type I, II, III and V (according Bianchi's classification), can be
obtained as expansions of the isometries in 2 dimensions. It is shown that in
general more than one semigroup will lead to the same result. It is impossible
to obtain the algebras of type IV, VI-IX as an expansion from the isometry
algebras in 2 dimensions. This means that the first set of algebras has
properties that can be obtained from isometries in 2 dimensions while the
second set has properties that are in some sense intrinsic in 3 dimensions. All
the results are checked with computer programs. This procedure can be
generalized to higher dimensions, which could be useful for diverse physical
applications.Comment: 23 pages, one of the authors is new, title corrected, finite
semigroup programming is added, the semigroup construction procedure is
checked by computer programs, references to semigroup programming are added,
last section is extended, appendix added, discussion of all the types of
Bianchi spaces is include
Generalized Chern-Simons higher-spin gravity theories in three dimensions
The coupling of spin-3 gauge fields to three-dimensional Maxwell and
-Lorentz gravity theories is presented. After showing how the usual spin-3
extensions of the and the Poincar\'e algebras in three dimensions can be
obtained as expansions of algebra,
the procedure is generalized so as to define new higher-spin symmetries.
Remarkably, the spin-3 extension of the Maxwell symmetry allows one to
introduce a novel gravity model coupled to higher-spin topological matter with
vanishing cosmological constant, which in turn corresponds to a flat limit of
the -Lorentz case. We extend our results to define two different families
of higher-spin extensions of three-dimensional Einstein gravity.Comment: version 3, 28 pages, accepted version in Nuclear Physics
Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
We show that infinite families of non-relativistic spin- symmetries in
dimensions, which include higher-spin extensions of the Bargmann,
Newton-Hooke, non-relativistic Maxwell, and non-relativistic AdS-Lorentz
algebras, can be obtained as Lie algebra expansions of two different spin-
extensions of the Nappi-Witten symmetry. These higher-spin Nappi-Witten
algebras, in turn, are obtained by means of In\"on\"u-Wigner contractions
applied to suitable direct product extensions of .
Conversely, we show that the same result can be obtained by considering
contractions of expanded algebras. The method can
be used to define non-relativistic higher-spin Chern-Simon gravity theories in
dimensions in a systematic way.Comment: 44 pages, typos corrected, references adde
Three-dimensional Hypergravity Theories and Semigroup Expansion Method
In this work we present novel and known three-dimensional hypergravity
theories which are obtained by applying the powerful semigroup expansion
method. We show that the expansion procedure considered here yields a
consistent way of coupling different three-dimensional Chern-Simons gravity
theories with massless spin- gauge fields. First, by expanding the
superalgebra with a particular semigroup a
generalized hyper-Poincar\'e algebra is found. Interestingly, the
hyper-Poincar\'e and hyper-Maxwell algebras appear as subalgebras of this
generalized hypersymmetry algebra. Then, we show that the generalized
hyper-Poincar\'e CS gravity action can be written as a sum of diverse
hypergravity CS Lagrangians. We extend our study to a generalized hyper-AdS
gravity theory by considering a different semigroup. Both generalized
hyperalgebras are then found to be related through an In\"on\"u-Wigner
contraction which can be seen as a generalization of the existing vanishing
cosmological constant limit between the hyper-AdS and hyper-Poincar\'e gravity
theories.Comment: 35 page
Three-dimensional teleparallel Chern-Simons supergravity theory
In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincaré supergravity in the vanishing cosmological limit. The extension of our results to supersymmetries is also explored
On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions
In this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-, the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the gravity theories. We extend our results to the and cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit