Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of ϱ-Minkowski

Fabiano, Giuseppe; Gubitosi, Giulia; Lizzi, Fedele; Scala, Luca; Vitale, Patrizia

doi:10.1007/jhep08(2023)220

Cited by 7 publications

(4 citation statements)

References 55 publications

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“…Namely, on the string theory side there is a class of deformations of the AdS 5 ×S 5 string specified by classical r matrices, known as Yang-Baxter (YB) deformations [60][61][62], which in the homogeneous case have Drinfel'd twisted symmetry [18,19]. 39 As originally conjectured in [19], our twist-noncommutative versions of SYM provide natural gauge theory duals to these homogeneous YB deformed strings, with each dual pair specified and determined by a classical r matrix.…”

Section: Ads/cftmentioning

confidence: 99%

“…These two examples of so-called Liealgebraic noncommutative structures are, among other names, known as λ-Minkowski and ρ-Minkowski space, see e.g. [34][35][36][37][38][39], and [40] for details on the twisted structure.…”

Section: Jhep12(2023)045mentioning

confidence: 99%

“…To complete this picture and include the single not-almost-abelian deformation of r 14 , we can use the general equivalence between homogeneous Yang-Baxter deformations and non-abelian T duality transformations [72][73][74], and similarly apply the correspondingtransformation to the standard D3 brane background. By definition, in the low energy limit this formally yields the desired Yang-Baxter deformations of AdS 5 ×S 5 in the closed 39 YB models date back to [63], see [48] for a recent pedagogical review. Inhomogeneous YB deformations, as originally considered in [60], lead to a trigonometric quantum deformed symmetry algebra [64,65].…”

Section: Ads/cftmentioning

confidence: 99%

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Gauge theory on twist-noncommutative spaces

Meier,

van Tongeren

2023

J. High Energ. Phys.

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We construct actions for four dimensional noncommutative Yang-Mills theory with star-gauge symmetry, with non-constant noncommutativity, to all orders in the noncommutativity. Our construction covers all noncommutative spaces corresponding to Drinfel’d twists based on the Poincaré algebra, including nonabelian ones, whose r matrices are unimodular. This includes particular Lie-algebraic and quadratic noncommutative structures. We prove a planar equivalence theorem for all such noncommutative field theories, and discuss how our actions realize twisted Poincaré symmetry, as well as twisted conformal and twisted supersymmetry, when applicable. Finally, we consider noncommutative versions of maximally supersymmetric Yang-Mills theory, conjectured to be AdS/CFT dual to certain integrable deformations of the AdS5 × S5 superstring.

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Section: Ads/cftmentioning

confidence: 99%

Section: Jhep12(2023)045mentioning

confidence: 99%

Section: Ads/cftmentioning

confidence: 99%

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Gauge theory on twist-noncommutative spaces

Meier,

van Tongeren

2023

J. High Energ. Phys.

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“…Noncommutative field and gauge theory on 𝜅-Minkowski spacetime are extensively investigated in the literature, and we refer the reader for more details to [67,[117][118][119][120][121]. The 𝜆-and 𝜚-Minkowski spacetimes with their symmetries have been recently investigated in [122][123][124].…”

Section: Angular Noncommutativity: the Case Of 𝜆-Minkowskimentioning

confidence: 99%

Introduction to noncommutative field and gauge theory

Vitale,

Adamo,

Dekhil

et al. 2024

Proceedings of Winter School of Theoretical Physics, Second and Third Training School of COST Action CA18108 "Quantum Gravity P

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These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory. Then, we review a specific approach to noncommutative field and gauge theory, which relies on the introduction of a derivations-based differential calculus. We focus on the cases of constant and linear noncommutativity, e.g., the Moyal spacetime and the so-called R 3 𝜆 , respectively. In particular, we review the 𝑔𝜑 4 scalar field theory and the 𝑈 (1) gauge theory on such noncommutative spaces. Finally, we discuss noncommutative spacetime symmetries from both the observer and particle point of view. In this context, the twist approach is reviewed and the 𝜆-Minkowski 𝑔𝜑 4 model is discussed.

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Gauge theory on ρ-Minkowski space-time

Maris,

Wallet

2024

J. High Energ. Phys.

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We construct a gauge theory model on the 4-dimensional ρ-Minkowski space-time, a particular deformation of the Minkowski space-time recently considered. The corresponding star product results from a combination of Weyl quantization map and properties of the convolution algebra of the special Euclidean group. We use noncommutative differential calculi based on twisted derivations together with a twisted notion of noncommutative connection. The twisted derivations pertain to the Hopf algebra of ρ-deformed translations, a Hopf subalgebra of the ρ-deformed Poincaré algebra which can be viewed as defining the quantum symmetries of the ρ-Minkowski space-time. The gauge theory model is left invariant under the action of the ρ-deformed Poincaré algebra. The kinetic part of the action is found to coincide with the one of the usual (commutative) electrodynamics.

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Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of ϱ-Minkowski

Cited by 7 publications

References 55 publications

Gauge theory on twist-noncommutative spaces

Gauge theory on twist-noncommutative spaces

Introduction to noncommutative field and gauge theory

Gauge theory on ρ-Minkowski space-time

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