Noncommutative Gauge Theory and Gravity in Three Dimensions

Chatzistavrakidis, Athanasios; Jonke, Larisa; Jurman, Danijel; Manolakos, G.; Manousselis, P.; Zoupanos, George

doi:10.1002/prop.201800047

Cited by 24 publications

(39 citation statements)

References 68 publications

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“…The group semi-direct product structure of the phase space T * SU (2) has been widely investigated in literature in many different contexts. Besides classical, well known applications, some of which we have already mentioned in the introduction, let us mention here applications in noncommutative geometry in relation to the quantization of the hydrogen atom[43], to the electron-monopole system[44], and, recently, to models on three-dimensional space-time with su(2) type non-commutativity[45,46,47,48] …”

mentioning

confidence: 99%

Doubling, T-Duality and Generalized Geometry: a simple model

Marotta

Pezzella

Vitale

2018

J. High Energ. Phys.

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A simple mechanical system, the three-dimensional isotropic rigid rotator, is here investigated as a 0+1 field theory, aiming at further investigating the relation between Generalized/Double Geometry on the one hand and Doubled World-Sheet Formalism/Double Field Theory, on the other hand. The model is defined over the group manifold of SU (2) and a dual model is introduced having the Poisson-Lie dual of SU (2) as configuration space. A generalized action with configuration space SL(2, C), i.e. the Drinfel'd double of the group SU (2), is then defined: it reduces to the original action of the rotator or to its dual, once constraints are implemented. The new action contains twice as many variables as the original. Moreover its geometric structures can be understood in terms of Generalized Geometry. keywords: Generalized Geometry, Double Field Theory, T-Duality, Poisson-Lie symmetry 1 Introduction Generalized Geometry (GG) was first introduced by N. J. Hitchin in ref. [1]. As the author himself states in his pedagogical lectures [2], it is based on two premises: the first consists in replacing the tangent bundle T of a manifold M with T ⊕ T * , a bundle with the same base space M but fibers given by the direct sum of tangent and cotangent spaces. The second consists in replacing the Lie bracket on the sections of T , which are vector fields, with the Courant bracket which involves vector fields and one-forms. The construction is then extended to general vector bundles E over M so to have E ⊕ E * and a suitable bracket for the sections of the new bundle.The formal setting of GG has recently attracted the interest of theoretical physicists in relation to Double Field Theory (DFT) [3]. We shall propose in this paper a model whose analysis can help to establish more rigorously a possible bridge between the two through the doubled world-sheet formalism that generates DFT.DFT has emerged as a proposal to incorporate T-duality [4,5], a peculiar symmetry of a compactified string on a d-torus T d in a (G, B)-background, as a manifest symmetry of the string effective field theory. In order to achieve this goal, the action of this field theory has to be generalized in such a way that the emerging carrier space of the dynamics be doubled with

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confidence: 99%

Doubling, T-Duality and Generalized Geometry: a simple model

Marotta

Pezzella

Vitale

2018

J. High Energ. Phys.

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“…However, the same problem that emerged in the 3-d case related to the anti-commutators of the generators of the algebra is encountered in this case, too [123,124,196] (see also [95]). The anti-commutators do not yield operators that belong to the algebra and this is exactly the case for the generators of SO (5).…”

Section: Determination Of the Gauge Group And Representation By 4 × 4mentioning

confidence: 80%

“…Therefore, it seems reasonable to combine the above two and construct a 3-d gravity model as a noncommutative gauge theory. The first step towards this direction is the identification of a suitable noncommutative space that will accommodate the gauge theory [123,124,196].…”

Section: -D Gravity As a Gauge Theory On Noncommutative Spacesmentioning

confidence: 99%

“…This article includes our contributions in the above aspect of noncommutative gravity. First, we review our approach for 3-d noncommutative gravity as a matrix model [123] (see also [124]), in which the corresponding space is the R 3 λ , introduced in [125] (for the construction of field theories on this space, see also [126]), which is in fact the foliation of the 3-d Euclidean space by fuzzy spheres of different radii. This space admits a natural action of SO(4) [127] and is the group we consider as the gauge group of the theory.…”

Section: Introductionmentioning

confidence: 99%

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Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

2019

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First, the Coset Space Dimensional Reduction scheme and the best particle physics model so far resulting from it are reviewed. Then, a higher-dimensional theory in which the extra dimensions are fuzzy coset spaces is described and a dimensional reduction to four-dimensional theory is performed. Afterwards, another scheme including fuzzy extra dimensions is presented, but this time the starting theory is four-dimensional while the fuzzy extra dimensions are generated dynamically. The resulting theory and its particle content is discussed. Besides the particle physics models discussed above, gravity theories as gauge theories are reviewed and then, the whole methodology is modified in the case that the background spacetimes are noncommutative. For this reason, specific covariant fuzzy spaces are introduced and, eventually, the program is written for both the 3-d and 4-d cases.

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“…In this paper we review the study of three-dimensional gravity as a noncommutative gauge theory [46]. First thing to do is the determination of the three-dimensional noncommutative spaces with the appropriate symmetry.…”

Section: Introductionmentioning

confidence: 99%

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

Jurman¹,

Manolakos²,

Manousselis³

et al. 2018

Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017)

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We plan to translate the successful description of three-dimensional gravity as a gauge theory in the noncommutative framework, making use of the covariant coordinates. We consider two specific three-dimensional fuzzy spaces based on SU(2) and SU(1,1), which carry appropriate symmetry groups. These are the groups we are going to gauge in order to result with the transformations of the gauge fields (dreibein, spin connection and two extra Maxwell fields due to noncommutativity), their corresponding curvatures and eventually determine the action and the equations of motion. Finally, we verify their connection to three-dimensional gravity.

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Noncommutative Gauge Theory and Gravity in Three Dimensions

Cited by 24 publications

References 68 publications

Doubling, T-Duality and Generalized Geometry: a simple model

Doubling, T-Duality and Generalized Geometry: a simple model

Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

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