1,721,027 research outputs found
AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit
Full text linkCarroll symmetries arise when the velocity of light is sent to zero (ultra-relativistic limit). In this paper, we present the construction of the three-dimensional Chern-Simons supergravity theory invariant under the so-called AdS Carroll superalgebra, which was obtained in the literature as a contraction of the AdS superalgebra. The action is characterized by two coupling constants. Subsequently, we study its flat limit, obtaining the three-dimensional Chern-Simons supergravity theory invariant under the super-Carroll algebra, which is a contraction of the Poincaré superalgebra. We apply the flat limit at the level of the superalgebra, Chern-Simons action, supersymmetry transformation laws, and field equations
Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity
Full text linkAbstract The purpose of this paper is to show that the so-called Maxwell superalgebra in four dimensions, which naturally involves the presence of a nilpotent fermionic generator, can be interpreted as a hidden superalgebra underlying N=1,D=4 supergravity extended to include a 2-form gauge potential associated to a 2-index antisymmetric tensor. In this scenario, the theory is appropriately discussed in the context of Free Differential Algebras (an extension of the Maurer–Cartan equations to involve higher-degree differential forms). The study is then extended to the Free Differential Algebra describing D=11 supergravity, showing that, also in this case, there exists a super-Maxwell algebra underlying the theory. The same extra spinors dual to the nilpotent fermionic generators whose presence is crucial for writing a supersymmetric extension of the Maxwell algebras, both in the D=4 and in the D=11 case, turn out to be fundamental ingredients also to reproduce the D=4 and D=11 Free Differential Algebras on ordinary superspace, whose basis is given by the supervielbein. The analysis of the gauge structure of the supersymmetric Free Differential Algebras is carried on taking into account the gauge transformations from the hidden supergroup-manifold associated with the Maxwell superalgebras
On the hidden symmetries of supergravity
Full text linkWe report on recent developments regarding the supersymmetric Free
Differential Algebra describing the vacuum structure of supergravity. We
focus on the emergence of a hidden superalgebra underlying the theory,
explaining the group-theoretical role played by the nilpotent fermionic
generator naturally appearing for consistency of the construction. We also
discuss the relation between this hidden superalgebra and other superalgebras
of particular relevance in the context of supergravity and superstring,
involving a fermionic generator with 32 components.Comment: Contribution to the Proceedings of the XIV International Workshop
"Lie Theory and its Applications in Physics" (LT-14), 20-25 June 2021,
organized from Sofia, Bulgaria (online). 12 page
N-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions
Full text linkIn this work we present the ultra-relativistic N-extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N-extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N, 0), with N even, and to N = (p, q), with p, q > 0. The N-extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N) extension of osp(2|N) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (l → ∞, being l the length parameter) of the aforementioned N-extended Chern-Simons AdS Carroll supergravities, in which we recover the ultra-relativistic N-extended (flat) Chern-Simons supergravity theories invariant under N-extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations
Cartan geometry, supergravity, and group manifold approach
Full text linkWe make a case for the unique relevance of Cartan geometry for gauge theories of gravity and supergravity. We introduce our discussion by recapitulating historical threads, providing motivations. In a first part we review the geometry of classical gauge theory, as a background for understanding gauge theories of gravity in terms of Cartan geometry. The second part introduces the basics of the group manifold approach to supergravity, hinting at the deep rooted connections to Cartan supergeometry. The contribution is intended, not as an extensive review, but as a conceptual overview, and hopefully a bridge between communities in physics and mathematics
Conformal gravity with totally antisymmetric torsion
Full text linkWe present a gauge theory of the conformal group in four spacetime dimensions with a nonvanishing torsion. In particular, we allow for a completely antisymmetric torsion, equivalent by Hodge duality to an axial vector whose presence does not spoil the conformal invariance of the theory, in contrast with claims of antecedent literature. The requirement of conformal invariance implies a differential condition (in particular, a Killing equation) on the aforementioned axial vector, which leads to a Maxwell-like equation in a four-dimensional curved background. We also give some preliminary results in the context of N=1 four-dimensional conformal supergravity in the geometric approach, showing that if we only allow for the constraint of vanishing supertorsion, all the other constraints imposed in the spacetime approach are a consequence of the closure of the Bianchi identities in superspace. This paves the way towards a future complete investigation of the conformal supergravity using the Bianchi identities in the presence of a nonvanishing (super)torsion
Generalized AdS-Lorentz deformed supergravity on a manifold with boundary
No full textThe purpose of this paper is to explore the supersymmetry invariance of a particular supergravity theory, which we refer to as D = 4 generalized AdS-Lorentz deformed supergravity, in the presence of a non-trivial boundary. In particular, we show that the so-called generalized minimal AdS-Lorentz superalgebra can be interpreted as a peculiar torsion deformation of (4 | 1) , and we present the construction of a bulk Lagrangian based on the aforementioned generalized AdS-Lorentz superalgebra. In the presence of a non-trivial boundary of space-time, that is when the boundary is not thought of as set at infinity, the fields do not asymptotically vanish, and this has some consequences on the invariances of the theory, in particular on supersymmetry invariance. In this work, we adopt the so-called rheonomic (geometric) approach in superspace and show that a supersymmetric extension of a Gauss-Bonnet-like term is required in order to restore the supersymmetry invariance of the theory. The action we end up with can be recast as a MacDowell-Mansouri-type action, namely as a sum of quadratic terms in the generalized AdS-Lorentz covariant super field-strengths
On the role of torsion and higher forms in off-shell supergravity
Full text linkWe elaborate on the presence of a nonvanishing totally antisymmetric
(super)torsion, equivalent to an axial vector, and higher forms in the "new
minimal" and "old minimal" off-shell formulations of ,
supergravity. We adopt the geometric superspace approach and study both the
geometric Lagrangian and the off-shell closure of the Bianchi identities in
this framework, showing how the aforementioned axial vector torsion contributes
to both the new and the old minimal set of auxiliary fields. In particular, to
reproduce the old minimal set within the geometric setup, we also introduce two
real auxiliary 3-form potentials.Comment: V2, 25 pages, some comments and references added, misprints correcte
An action principle for the Einstein–Weyl equations
Full text linkA longstanding open problem in mathematical physics has been that of finding an action principle for the Einstein–Weyl (EW) equations. In this paper, we present for the first time such an action principle in three dimensions in which the Weyl vector is not exact. More precisely, our model contains, in addition to the Weyl nonmetricity, a traceless part. If the latter is (consistently) set to zero, the equations of motion boil down to the EW equations. In particular, we consider a metric affine f(R) gravity action plus additional terms involving Lagrange multipliers and gravitational Chern–Simons contributions. In our framework, the metric and the connection are considered as independent objects, and no a priori assumptions on the nonmetricity and the torsion of the connection are made. The dynamics of the Weyl vector turns out to be governed by a special case of the generalized monopole equation, which represents a conformal self-duality condition in three dimensions
On SIR-type epidemiological models and population heterogeneity effects
Full text linkIn this paper we elaborate on homogeneous and heterogeneous SIR-type epidemiological models. We find an unexpected correspondence between the epidemic trajectory of a transmissible disease in a homogeneous SIR-type model and radial null geodesics in the Schwarzschild spacetime. We also discuss modeling of population heterogeneity effects by considering both a one-and two-parameter gamma-distributed function for the initial susceptibility distribution, and deriving the associated herd immunity threshold. We furthermore describe how mitigation measures can be taken into account by model fitting
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