SO(2,3)★ Noncommutative Gravity: Coupling with Matter Fields

AbstractWe define a new homotopy algebraic structure, that we call a braided $$L_\infty $$ L ∞ -algebra, and use it to systematically construct a new class of noncommutative field theories, that we call braided field theories. Braided field theories have gauge symmetries which realize a braided Lie algebra, whose Noether identities are inhomogeneous extensions of the classical identities, and which do not act on the solutions of the field equations. We use Drinfel’d twist deformation quantization techniques to generate new noncommutative deformations of classical field theories with braided gauge symmetries, which we compare to the more conventional theories with star-gauge symmetries. We apply our formalism to introduce a braided version of general relativity without matter fields in the Einstein–Cartan–Palatini formalism. In the limit of vanishing deformation parameter, the braided theory of noncommutative gravity reduces to classical gravity without any extensions.

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Introducing matter fields in model of noncommutative gravity

Facta universitatis - series Physics Chemistry and Technology ◽

10.2298/fupct1901031d ◽

2019 ◽

Vol 17 (1, spec.issue) ◽

pp. 31-42

Author(s):

Marija Dimitrijevic-Ciric ◽

Dragoljub Gocanin ◽

Nikola Konjik ◽

Voja Radovanovic

Keyword(s):

Landau Levels ◽

Gauge Fields ◽

Significant Feature ◽

Yang Mills ◽

Enveloping Algebra ◽

Algebra Approach ◽

Background Magnetic Field ◽

Gauge Fixing ◽

Noncommutative Gravity ◽

Matter Fields

Theory founded on SO(2,3)* gauge symmetry. One significant feature of this approach is that gravitational field, given by the vierbein, becomes manifest only after a suitable gauge fixing and it is formally united with other gauge fields. Starting from a model of pure noncommutative gravity, we extend it by introducing fermions and Yang-Mills gauge field. Using the enveloping algebra approach and the Seiberg-Witten map we construct corresponding actions and expand them perturbatively in powers of the canonical noncommutativity parameter ???. Unlike in the case of pure noncommutative gravity, first non-vanishing noncommutative corrections are linear in the noncommutativity parameter and they describe the coupling of matter and gauge fields with gravity due to spacetime noncommutativity. This is augmented by the fact that some of these corrections pertain even in flat spacetime where they induce potentially observable noncommutative deformations. We discuss the effects of noncommutativity on electron?s dispersion relation in the presence of constant background magnetic field - Landau levels. Our results could be useful for further investigation of phenothe menological consequences of spacetime noncommutativity.

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Shape Dynamics and the Linking Theory

10.1093/oso/9780198789475.003.0012 ◽

2018 ◽

Author(s):

Flavio Mercati

Keyword(s):

Phase Space ◽

Degrees Of Freedom ◽

Line Element ◽

Hamiltonian Formulation ◽

Operational Definition ◽

Extended Phase Space ◽

Extended Phase ◽

Problem Of Time ◽

Definition Of ◽

Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

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Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

Journal of High Energy Physics ◽

10.1007/jhep07(2021)064 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Keiya Ishiguro ◽

Tatsuo Kobayashi ◽

Hajime Otsuka

Keyword(s):

String Theory ◽

Hierarchical Structure ◽

Matter Field ◽

Heterotic String ◽

Heterotic String Theory ◽

Kähler Metric ◽

Yukawa Couplings ◽

String Compactifications ◽

Kahler Metric ◽

Matter Fields

Abstract We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

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