Deformed Weitzenböck Connections and Double Field Theory

Penas, Victor Alejandro

doi:10.1002/prop.201800077

Cited by 6 publications

(4 citation statements)

References 66 publications

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“…The analysis of this paper might also be extended in other directions. In particular, it would be interesting to generalize the construction of [71] concerning the Chern-Simons formulation of threedimensional gravity involving torsion and nonmetricity, and the recent results presented in [88] in the context of double field theory. One could also investigate possible generalizations of [85,86].…”

Section: Discussionmentioning

confidence: 99%

Einstein manifolds with torsion and nonmetricity

Klemm

Ravera

2020

Phys. Rev. D

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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 in d dimensions with nonvanishing torsion that has both a trace and a traceless part, and analyze the conformal invariance 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 (i.e., conformal gravity) action describe the same dynamics. Then, we consider the Einstein-Hilbert action coupled to a three-form field strength and shew that its equations of motion imply that the manifold is Einstein with skew-symmetric torsion.In the 19th century, the branches of mathematics and physics experienced an extraordinary progress with the emergence of non-Euclidean geometry. In particular, the development of Riemannian geometry led to many important results, among which the rigorous mathematical formulation of Einstein's general relativity.In spite of the success and predictive power of general relativity, there are still some open problems and questions, whose understanding and solution may need the formulation of a new theoretical framework as well as generalizations and extensions of Riemannian geometry. One possible way of generalizing Riemannian geometry consists in allowing for nonvanishing torsion and nonmetricity (metric affine gravity) [1] (see also [2] and the recent work [3]). There are several physical (and mathematical) reasons which motivate the introduction of torsion or nonmetricity in the context of gravitational theories (see [1] for details). For instance, nonmetricity is a measure for the violation of local Lorentz invariance, which has been attracting some interest recently. Furthermore, nonmetricity and torsion find applications in the theory of defects in crystals, where, in particular, nonmetricity describes the density of point defects, while torsion is interpreted as density in line defects [4]. Moreover, as recently shown in [5], incorporating torsion and nonmetricity may allow to explore new physics associated with defects in a hypothetical spacetime microstructure. Further applications include quantum gravity [6] and cosmology [7][8][9].Historically, a remarkable generalization of ...

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Section: Discussionmentioning

confidence: 99%

Einstein manifolds with torsion and nonmetricity

Klemm

Ravera

2020

Phys. Rev. D

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“…This is very reminiscent of the notion of a Weitzenböck connection, as used in teleparallel gravity and related theories where gravity is 'all torsion and no curvature'. We also remark that Weitzenböck connections make an appearance in double field theory (see for example [32] and references therein). These considerations lead to the following notion.…”

Section: Odd Weitzenböck Connectionsmentioning

confidence: 90%

Odd connections on supermanifolds: existence and relation with affine connections

Bruce¹,

Grabowski²

2020

J. Phys. A: Math. Theor.

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The notion of an odd quasi-connection on a supermanifold, which is loosely an affine connection that carries non-zero Grassmann parity, is examined. Their torsion and curvature are defined, however, in general, they are not tensors. A special class of such generalised connections, referred to as odd connections in this paper, have torsion and curvature tensors. Part of the structure is an odd involution of the tangent bundle of the supermanifold and this puts drastic restrictions on the supermanifolds that admit odd connections. In particular, they must have equal number of even and odd dimensions. Amongst other results, we show that an odd connection is defined, up to an odd tensor field of type (1, 2), by an affine connection and an odd endomorphism of the tangent bundle. Thus, the theory of odd connections and affine connections are not completely separate theories. As an example relevant to physics, it is shown that N = 1 super-Minkowski spacetime admits a natural odd connection.

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“…• It would be useful to extend the notion of supersymmetric modified gravities into the language of T-duality invariant cosmological frameworks [30]- [34], where the notion of generalized geometry arises. The agreement between Riemannian geometries and the generalized geometry required to manifest T-duality invariance was studied in [35] and more recently in [36]. Following these lines it would be nice to extend the construction of black/worm holes [37]- [38] but considering T-duality invariant approaches as in [39].…”

Section: Discussionmentioning

confidence: 99%

${\cal N}=1$ supersymmetry in $4D$ gravity with torsion and non-metricity

Bejarano¹,

Lescano²

2022

Preprint

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We study the inclusion of fermionic degrees of freedom and N = 1 supersymmetry in 4-dimensional manifolds with arbitrary torsion and non-metricity tensors deforming the connection. We inspect the closure of local diffeomorphism, Lorentz and supersymmetric transformations on the vielbein and gravitino at leading order in fermions. The closure of a pair of supersymmetric transformations acting on the vielbein restricts the form of the spin connection. The dependency of the latter on the fundamental fields is exclusively given by the vielbein, up to Lorentz and/or diffeomorphisms brackets, independently of the torsion or non-metricity deformations of the affine connection, which is not restricted by supersymmetry at this order. We have then studied the couple of the Rarita-Schwinger theory to a generic gravitational Lagrangian; the supersymmetric variation of the former restricts the form of the bosonic Lagrangian in order to accomplish invariance. Special cases where Rµν ab = 0, Qµνρ = 0 or Tµν ρ = 0 are provided.

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Deformed Weitzenböck Connections and Double Field Theory

Cited by 6 publications

References 66 publications

Einstein manifolds with torsion and nonmetricity

Einstein manifolds with torsion and nonmetricity

Odd connections on supermanifolds: existence and relation with affine connections

${\cal N}=1$ supersymmetry in $4D$ gravity with torsion and non-metricity

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