5,449 research outputs found
Hidden Role of Maxwell Superalgebras in the Free Differential Algebras of D=4 and D=11 Supergravity
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.Comment: 23 pages, misprints corrected, some comments added, version published
in The European Physical Journal C. Contains some text overlap with the
author's PhD thesis arXiv:1802.0660
More on the Hidden Symmetries of 11D Supergravity
In this paper we clarify the relations occurring among the osp(1|32) algebra,
the M-algebra and the hidden superalgebra underlying the Free Differential
Algebra of D=11 supergravity (to which we will refer as DF-algebra) that was
introduced in the literature by D'Auria and Fr\'e in 1981 and is actually a
(Lorentz valued) central extension of the M-algebra including a nilpotent
spinor generator, Q'. We focus in particular on the 4-form cohomology in 11D
superspace of the supergravity theory, strictly related to the presence in the
theory of a 3-form . Once formulated in terms of its hidden
superalgebra of 1-forms, we find that can be decomposed into the sum
of two parts having different group-theoretical meaning: One of them allows to
reproduce the FDA of the 11D Supergravity due to non-trivial contributions to
the 4-form cohomology in superspace, while the second one does not contribute
to the 4-form cohomology, being a closed 3-form in the vacuum, defining however
a one parameter family of trilinear forms invariant under a symmetry algebra
related to osp(1|32) by redefining the spin connection and adding a new
Maurer-Cartan equation. We further discuss about the crucial role played by the
1-form spinor (dual to the nilpotent generator Q') for the 4-form
cohomology of the eleven dimensional theory on superspace.Comment: Title and abstract changed to better represent the content, some
points clarified, mainly in Section 2 and in the concluding section,
references added. Version accepted for publication on Physics Letters
Minimal Supergravity and the supersymmetry of Arnold-Beltrami Flux branes
In this paper we study some properties of the newly found Arnold-Beltrami
flux-brane solutions to the minimal supergravity. To this end we first
single out the appropriate Free Differential Algebra containing both a gauge
-form and a gauge -form : then we
present the complete rheonomic parametrization of all the generalized
curvatures. This allows us to identify two-brane configurations with
Arnold-Beltrami fluxes in the transverse space with exact solutions of
supergravity and to analyze the Killing spinor equation in their background. We
find that there is no preserved supersymmetry if there are no additional
translational Killing vectors. Guided by this principle we explicitly construct
Arnold-Beltrami flux two-branes that preserve , and of the
original supersymmetry. Two-branes without fluxes are instead BPS states and
preserve supersymmetry. For each two-brane solution we carefully study
its discrete symmetry that is always given by some appropriate crystallographic
group . Such symmetry groups are transmitted to the
gauge theories on the brane world--volume that occur in the gauge/gravity
correspondence. Furthermore we illustrate the intriguing relation between gauge
fluxes in two-brane solutions and hyperinstantons in topological
sigma-models.Comment: 56 pages, LaTeX source, 8 jpg figures, typos correcte
Group Theoretical Hidden Structure of Supergravity Theories in Higher Dimensions
The purpose of my PhD thesis is to investigate different group theoretical
and geometrical aspects of supergravity theories. To this aim, several research
topics are explored: On one side, the construction of supergravity models in
diverse space-time dimensions, including the study of boundary contributions,
and the disclosure of the hidden gauge structure of these theories; on the
other side, the analysis of the algebraic links among different superalgebras
related to supergravity theories.
In the first three chapters, we give a general introduction and furnish the
theoretical background necessary for a clearer understanding of the thesis. We
then move to the original results of my PhD research activity: We start from
the development of the so called -Lorentz supergravity in by
adopting the so called rheonomic approach and discuss on boundary contributions
to the theory. Subsequently, we focus on the analysis of the hidden gauge
structure of supersymmetric Free Differential Algebras. More precisely, we
concentrate on the hidden superalgebras underlying and
supergravities, exploring the symmetries hidden in the theories and the
physical role of the nilpotent fermionic generators naturally appearing in the
aforementioned superalgebras. After that, we move to the pure algebraic and
group theoretical description of (super)algebras, focusing on new analytic
formulations of the so called -expansion method. The final chapter contains
the summary of the results of my doctoral studies presented in the thesis and
possible future developments. In the Appendices, we collect notation, useful
formulas, and detailed calculations.Comment: 204 pages, 5 figures. Thesis discussed on February 8, 2018 for the
Ph.D title achievement in Physics, carried out in the Politecnico di Torino
Ph.D program in Physics (cycle 30th). It contains results and material
already published in arXiv:1511.06245, arXiv:1606.07328, arXiv:1607.00373,
arXiv:1609.05042, arXiv:1611.05812, arXiv:1701.04234, arXiv:1705.06251,
arXiv:1801.0886
On the geometric approach to the boundary problem in supergravity
We review the geometric superspace approach to the boundary problem in supergravity, retracing the geometric construction of four-dimensional supergravity Lagrangians in the presence of a non-trivial boundary of spacetime. We first focus on pure N = 1 and N = 2 theories with negative cosmological constant. Here, the supersymmetry invariance of the action requires the addition of topological (boundary) contributions which generalize at the supersymmetric level the Euler-Gauss-Bonnet term. Moreover, one finds that the boundary values of the super field-strengths are dynamically fixed to constant values, corresponding to the vanishing of the OSp(N |4)-covariant supercurvatures at the boundary. We then consider the case of vanishing cosmological constant where, in the presence of a non-trivial boundary, the inclusion of boundary terms involving additional fields, which behave as auxiliary fields for the bulk theory, allows to restore supersymmetry. In all the cases listed above, the full, supersymmetric Lagrangian can be recast in a MacDowell-Mansouri(-like) form. We then report on the application of the results to specific problems regarding cases where the boundary is located asymptotically, relevant for a holographic analysis
An Analytic Method for -Expansion involving Resonance and Reduction
In this paper we describe an analytic method able to give the multiplication
table(s) of the set(s) involved in an -expansion process (with either
resonance or -resonant-reduction) for reaching a target Lie (super)algebra
from a starting one, after having properly chosen the partitions over subspaces
of the considered (super)algebras. This analytic method gives us a simple set
of expressions to find the partitions over the set(s) involved in the process.
Then, we use the information coming from both the initial (super)algebra and
the target one for reaching the multiplication table(s) of the mentioned
set(s). Finally, we check associativity with an auxiliary computational
algorithm, in order to understand whether the obtained set(s) can describe
semigroup(s) or just abelian set(s) connecting two (super)algebras. We also
give some interesting examples of application, which check and corroborate our
analytic procedure and also generalize some result already presented in the
literature.Comment: v3, 47 pages, misprints corrected in Fortschritte der Physik,
Published online 7 November 201
Conformal gravity with totally antisymmetric torsion
We 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
An action principle for the Einstein-Weyl equations
A 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
Generalized AdS-Lorentz deformed supergravity on a manifold with boundary
The 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 osp(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.Comment: 32 pages. Version accepted for publication in The European Physical
Journal Plus (EPJP), Eur. Phys. J. Plus (2018) 133: 514. The final
publication is available at Springer via
https://doi.org/10.1140/epjp/i2018-12335-0. arXiv admin note: text overlap
with arXiv:1802.0660
Einstein manifolds with torsion and nonmetricity
Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds whose symmetrized Ricci tensor is proportional to the metric) in d dimensions with nonvanishing torsion that has both a trace and a traceless part, and analyze invariance under extended conformal transformations of the corresponding field equations. Then, we compare our results to the case of Einstein manifolds with zero torsion and nonvanishing nonmetricity, where the latter is given in terms of the Weyl vector (Einstein-Weyl spaces). We find that the trace part of the torsion can alternatively be interpreted as the trace part of the nonmetricity. The analysis is subsequently extended to Einstein spaces with both torsion and nonmetricity, where we also discuss the general setting in which the nonmetricity tensor has both a trace and a traceless part. Moreover, we consider and investigate actions involving scalar curvatures obtained from torsionful or nonmetric connections, analyzing their relations with other gravitational theories that appeared previously in the literature. In particular, we show that the Einstein-Cartan action and the scale invariant gravity (also known as conformal gravity) action describe the same dynamics. Then, we consider the Einstein-Hilbert action coupled to a three-form field strength and show that its equations of motion imply that the manifold is Einstein with totally antisymmetric torsion
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