Covariant quiver gauge theories

Szabo, Richard J.; Valdivia, Omar

doi:10.1007/jhep06(2014)144

Cited by 12 publications

(28 citation statements)

References 43 publications

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“…The torsion equations follow from the variation of (6) w.r.t. the spin connection ω ab λ , not constrained to be the Levi-Civita connection (7), yielding…”

Section: Equations Of Motionmentioning

confidence: 99%

“…having used the same unit vector n α (1) in (18) as that given by (17). We restrict our attention to the torsion-free case, substituting the Ansatz (16) in the Levi-Civita connection (7) and calculating the resulting components of the curvature. Using this reduced spin connection and the Ansatz (18)- (19), we calculate the reduced (covariant) derivatives of the fields (φ a , φ).…”

Section: The Solutions 31 the Ansatzmentioning

confidence: 99%

“…Apart from the definition in Ref [7]. being restricted to odd dimensions, there is another important difference with with our formulation.…”

mentioning

confidence: 99%

“…being restricted to odd dimensions, there is another important difference with with our formulation. In our case the dimensional reduction is carried out on the gauge invariant CP density yielding the HCP density, while in[7] it is the CS density in the (higher) odd dimensions that is subjected to dimensional reduction. While the results happen to be similar, there is no guarantee they should agree since subjecting a gauge variant CS density to symmetry imposition as done in[7] problematic.2 These choices coincide with the representations that yield monopoles on IR d described in[4]3 We do not make a choice for the signature of the space at this stage.…”

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confidence: 99%

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A Higgs–Chern–Simons gravity model in 2 + 1 dimensions

Radu

Tchrakian

2018

Class. Quantum Grav.

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We study a gravity model in 2 + 1 dimensions, arising from a generalized Chern-Simons (CS) density we call a Higgs-Chern-Simons (HCS) density. This generalizes the construction of gravitational systems resulting from non-Abelian CS densities in all odd dimensions. The new HCS densities employed here are arrived at by the usual one-step descent of new Higgs-Chern-Pontryagin (HCP) densities, the latter resulting from the dimensional reduction of Chern-Pontryagin (CP) densities in some even dimension, such that in any given dimension (including even) there is an infinite tower of such models. Here, we restrict our attention to the lowest dimension, 2 + 1, and to the simplest such model resulting from the dimensional reduction of the 3-rd CP density. We construct a black hole (BH) solution in closed form, generalizing the familiar BTZ BH. We also study the electrically charged BH solution of the same model augmented with a Maxwell term, and contrast this solution with the electrically charged BTZ BH, specifically concering their respective thermodynamic properties.

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“…The torsion equations follow from the variation of (6) w.r.t. the spin connection ω ab λ , not constrained to be the Levi-Civita connection (7), yielding…”

Section: Equations Of Motionmentioning

confidence: 99%

Section: The Solutions 31 the Ansatzmentioning

confidence: 99%

“…Apart from the definition in Ref [7]. being restricted to odd dimensions, there is another important difference with with our formulation.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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A Higgs–Chern–Simons gravity model in 2 + 1 dimensions

Radu

Tchrakian

2018

Class. Quantum Grav.

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“…Examples of these are the Bogomol'nyi equations for magnetic monopoles in 3 dimensions and the vortex equation in 2 dimensions, as well as many other important integrable systems and soliton equations. In the context of model building, some physicists have applied for a long time the method of 'coset-space dimensional reduction' in the construction of gauge unified theories (see, e.g., [15,7,20,26]). …”

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confidence: 99%

A Tannakian approach to dimensional reduction of principal bundles

Álvarez-Cónsul

Biswas

Garcı́a-Prada

2017

Journal of Geometry and Physics

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Abstract. Let P be a parabolic subgroup of a connected simply connected complex semisimple Lie group G. Given a compact Kähler manifold X, the dimensional reduction of G-equivariant holomorphic vector bundles over X × G/P was carried out by the first and third authors [2]. This raises the question of dimensional reduction of holomorphic principal bundles over X × G/P . The method used for equivariant vector bundles does not generalize to principal bundles. In this paper, we adapt to equivariant principal bundles the Tannakian approach of Nori, to describe the dimensional reduction of Gequivariant principal bundles over X × G/P , and to establish a Hitchin-Kobayashi type correspondence. In order to be able to apply the Tannakian theory, we need to assume that X is a complex projective manifold. IntroductionDimensional reduction is a very powerful construction in the context of gauge theory, both in physics and geometry. Many important gauge-theoretic equations appear as symmetric solutions of fundamental equations for connections, like the instanton equations on Riemannian 4-manifolds. Examples of these are the Bogomol'nyi equations for magnetic monopoles in 3 dimensions and the vortex equation in 2 dimensions, as well as many other important integrable systems and soliton equations. In the context of model building, some physicists have applied for a long time the method of 'coset-space dimensional reduction' in the construction of gauge unified theories (see, e.g., [15,7,20,26]).In [16,17,11,1] the dimensional reduction techniques were brought into the context of holomorphic vector bundles over Kähler manifolds, to study the dimensional reduction of stable SL(2, C)-equivariant bundles over X × P 1 and the corresponding Hermitian-YangMills equations, where X is a compact Kähler manifold and P 1 is the Riemann sphere. In [2] this construction was generalised to G-equivariant vector bundles on X ×G/P , where G is a connected simply connected complex semisimple Lie group and P ⊂ G is a parabolic subgroup. These gave rise to quiver bundles with relations, that is representations of a quiver with relations in the category of vector bundles, where the quiver with relations (Q, K) is determined by P . In particular when X is a point, one has a description of 2000 Mathematics Subject Classification. 53C07, 14D21, 16G20.

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Mimetic Einstein-Cartan-Sciama-Kibble (ECSK) gravity

Izaurieta

Medina

Merino

et al. 2020

J. High Energ. Phys.

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In this paper, we formulate the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Sciama-Kibble (ECSK) gravity. We consider different possibilities on how torsion is affected by Weyl transformations and discuss how this translates into the interpolation between two different Weyl transformations of the spin connection, parameterized with a zero-form parameter λ. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conservation of the mimetic stress-energy tensor and show that the trace of the total stress-energy tensor is not null but depends on both, the value of λ and spacetime torsion.

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Covariant quiver gauge theories

Cited by 12 publications

References 43 publications

A Higgs–Chern–Simons gravity model in 2 + 1 dimensions

A Higgs–Chern–Simons gravity model in 2 + 1 dimensions

A Tannakian approach to dimensional reduction of principal bundles

Mimetic Einstein-Cartan-Sciama-Kibble (ECSK) gravity

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