Supergravity in the Group‐Geometric Framework: A Primer

Castellani, Leonardo

doi:10.1002/prop.201800014

Cited by 12 publications

(14 citation statements)

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“…This framework is well suited also to the case of p-form fields coupled to (super)gravity, and a group-geometric approach has been developed since the late 70's based on free differential algebras (FDA's) [1]- [8] (for a recent review see for ex. [9] ). In the 80's a form-Hamiltonian formalism was proposed in a series of papers [10]- [14], where momenta π conjugated to basic p-form fields φ are defined as "derivatives" of the d-form Lagrangian with respect to the "velocities" dφ, and the d-form Hamiltonian is defined as H = (dφ)π−L.…”

Section: Introductionmentioning

confidence: 99%

Covariant Hamiltonian for gravity coupled top-forms

Castellani

D’Adda

2020

Phys. Rev. D

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We review the covariant canonical formalism initiated by D'Adda, Nelson and Regge in 1985, and extend it to include a definition of form-Poisson brackets (FPB) for geometric theories coupled to p-forms, gauging free differential algebras. The form-Legendre transformation and the form-Hamilton equations are derived from a d-form Lagrangian with p-form dynamical fields φ. Momenta are defined as derivatives of the Lagrangian with respect to the "velocities" dφ and no preferred time direction is used. Action invariance under infinitesimal form-canonical transformations can be studied in this framework, and a generalized Noether theorem is derived, both for global and local symmetries.We apply the formalism to vielbein gravity in d = 3 and d = 4. In the d = 3 theory we can define form-Dirac brackets, and use an algorithmic procedure to construct the canonical generators for local Lorentz rotations and diffeomorphisms. In d = 4 the canonical analysis is carried out using FPB, since the definition of form-Dirac brackets is problematic. Lorentz generators are constructed, while diffeomorphisms are generated by the Lie derivative.A "doubly covariant" hamiltonian formalism is presented, allowing to maintain manifest Lorentz covariance at every stage of the Legendre transformation. The idea is to take curvatures as "velocities" in the definition of momenta.

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Section: Introductionmentioning

confidence: 99%

Covariant Hamiltonian for gravity coupled top-forms

Castellani

D’Adda

2020

Phys. Rev. D

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“…These theories possess local supersymmetry and, if the superalgebra contains the Lorentz or (A)dS algebra, represented by a Lorentz connection and a vielbein, they also include gravity. The gauge fields associated with the SUSY generators are spin 3/2 fermions (gravitini), while the internal symmetry has standard spin 1 gauge fields [15,16]. These CS supergravity theories are covariant under general coordinate transformations, they do not exhibit matching SUSY pairs and, although they are topological in a certain sense, they describe propagating degrees of freedom [1].…”

Section: Standard and Cs Supergravitiesmentioning

confidence: 99%

Unconventional SUSY and Conventional Physics: A Pedagogical Review

et al. 2021

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In supersymmetric extensions of the Standard Model, the observed particles come in fermion–boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles, not a single supersymmetric pair has been reported to date. Although a hypothetical SUSY breaking mechanism, operating at high energy inaccessible to current experiments cannot be ruled out, this reduces SUSY’s predictive power and it is unclear whether SUSY, in its standard form, can help reducing the remaining puzzles of the standard model (SM). Here we argue that SUSY can be realized in a different way, connecting spacetime and internal bosonic symmetries, combining bosonic gauge fields and fermionic matter particles in a single gauge field, a Lie superalgebra-valued connection. In this unconventional representation, states do not come in SUSY pairs, avoiding the doubling of particles and fields and SUSY is not a fully off-shell invariance of the action. The resulting systems are remarkably simple, closely resembling a standard quantum field theory and SUSY still emerges as a contingent symmetry that depends on the features of the vacuum/ground state. We illustrate the general construction with two examples: (i) A 2 + 1 dimensional system based on the osp(2,2|2) superalgebra, including Lorentz and u(1) generators that describe graphene; (ii) a supersymmetric extension of 3 + 1 conformal gravity with an SU(2,2|2) connection that describes a gauge theory with an emergent chiral symmetry breaking, coupled to gravity. The extensions to higher odd and even dimensions, as well as the extensions to accommodate more general internal symmetries are also outlined.

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“…The parametrizations (28a)-(28g) we have obtained above allow to derive the supersymmetry transformations in a direct way. Indeed, in the geometric framework we have adopted, the transformations on space-time are given by (see [23,24] and [25] for details):…”

Section: Supersymmetry Transformation Laws Obtained Within the Geometmentioning

confidence: 99%

“…More recently, in [22] the authors constructed the N = 1 and N = 2, D = 4 supergravity theories with negative cosmological constant in the presence of a non-trivial boundary in a geometric framework (extending to superspace the geometric approach of [11][12][13][14][15]): Precisely, they generalized the so-called rheonomic (geometric) approach to supergravity [23] (see also [24,25] for recent reviews of this framework) in the presence of a non-trivial boundary and they added proper boundary terms to the Lagrangian in order to restore the supersymmetry invariance of the theory. In particular, the authors found that the supersymmetry invariance of the full Lagrangian (understood as bulk plus boundary contributions) is recovered with the introduction of a supersymmetric extension of the Gauss-Bonnet term.…”

Section: Introductionmentioning

confidence: 99%

Generalized AdS-Lorentz deformed supergravity on a manifold with boundary

Banaudi

Ravera

2018

Eur. Phys. J. Plus

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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. * alessandro.banaudi@mi.infn.it † lucrezia.ravera@mi.infn.it 1 The S-expansion method [31] is based on combining the multiplication law of a semigroup S with the structure constants of a Lie (super)algebra g, in such a way to end up with a new, larger, Lie (super)algebra g S = S × g, that is called the S-expanded (super)algebra (see also [32] for an analytic method for performing S-expansion).

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Supergravity in the Group‐Geometric Framework: A Primer

Cited by 12 publications

References 92 publications

Covariant Hamiltonian for gravity coupled top-forms

Covariant Hamiltonian for gravity coupled top-forms

Unconventional SUSY and Conventional Physics: A Pedagogical Review

Generalized AdS-Lorentz deformed supergravity on a manifold with boundary

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