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Related papers: Gauge transformations for twisted spectral triples

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The spectral torsion is defined by three vector fields and Dirac operators and the noncommutative residue. Motivated by the spectral torsion and the one form rescaled Dirac operator, we give some new spectral torsion which is the extension…

Differential Geometry · Mathematics 2025-05-30 Jian Wang , Yong Wang

We introduce the notion of a twisted differential operator of given radius relative to an endomorphism $$\sigma$$ of an affinoid algebra A. We show that this notion is essentially independent of the choice of the endomorphism $$\sigma$$. As…

Algebraic Geometry · Mathematics 2020-02-12 Bernard Le Stum , Adolfo Quirós

In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic sigma-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a…

High Energy Physics - Theory · Physics 2017-01-17 Athanasios Chatzistavrakidis , Andreas Deser , Larisa Jonke , Thomas Strobl

We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for…

High Energy Physics - Theory · Physics 2017-03-15 Francisco Correa , Vit Jakubsky

In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and…

High Energy Physics - Theory · Physics 2015-09-01 Wonyoung Cho , J. J. Fernández-Melgarejo , Imtak Jeon , Jeong-Hyuck Park

We show that the equations of motion for (free) integer higher spin gauge fields can be formulated as twisted self-duality conditions on the higher spin curvatures of the spin-$s$ field and its dual. We focus on the case of four spacetime…

High Energy Physics - Theory · Physics 2018-02-02 Marc Henneaux , Sergio Hörtner , Amaury Leonard

Dirac's approach to gauge symmetries is discussed. We follow closely the steps that led him from his conjecture concerning the generators of gauge transformations {\it at a given time} --to be contrasted with the common view of gauge…

History and Philosophy of Physics · Physics 2007-05-23 Josep M. Pons

We develop a diagrammatic perturbation theory to account for the emergence of moir\'e bands in the continuum model of twisted bilayer graphene. Our framework is build upon treating the moir\'e potential as a perturbation that transfers…

Mesoscale and Nanoscale Physics · Physics 2024-07-30 Federico Escudero

We extend naturally the spectral triple which define noncommutative geometry (NCG) in order to incorporate supersymmetry and obtain supersymmetric Dirac operator D_M which acts on Minkowskian manifold. Inversely, we can consider the…

High Energy Physics - Theory · Physics 2014-05-07 Satoshi Ishihara , Hironobu Kataoka , Atsuko Matsukawa , Hikaru Sato , Masafumi Shimojo

We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for…

Mathematical Physics · Physics 2024-06-19 Fabien Besnard , Shane Farnsworth

We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra A and the noncommutative…

High Energy Physics - Theory · Physics 2009-10-31 G. Landi , F. Lizzi , R. J. Szabo

We study the twisted reality condition of Math. Phys. Anal. Geom. 19 (2016),no. 3, Art. 16, for spectral triples, in particular with respect to the product and the commutant. Motivated by this we present the procedure, which allows one to…

Quantum Algebra · Mathematics 2019-03-08 Tomasz Brzezinski , Ludwik Dabrowski , Andrzej Sitarz

We have obtained the supersymmetric extension of spectral triple which specify a noncommutative geometry(NCG). We assume that the functional space H constitutes of wave functions of matter fields and their superpartners included in the…

High Energy Physics - Theory · Physics 2014-12-31 Satoshi Ishihara , Hironobu Kataoka , Atsuko Matsukawa , Hikaru Sato , Masafumi Shimojo

Gauge symmetry breaking by boundary conditions is studied in a general warped geometry in five dimensions. It has been suggested that a wider class of boundary conditions is allowed by requiring only vanishing surface terms when deriving…

High Energy Physics - Theory · Physics 2008-11-26 Norisuke Sakai , Nobuhiro Uekusa

In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…

Spectral Theory · Mathematics 2022-09-07 Pablo Miranda , Daniel Parra , Georgi Raikov

We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our…

High Energy Physics - Theory · Physics 2009-04-23 Hajime Aoki , Jun Nishimura , Yoshiaki Susaki

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

Spectral Theory · Mathematics 2008-01-21 K. Veselic

By twisting the spectral triple of a riemannian spin manifold, we show how to generate an orthogonal and geodesic preserving torsion from a torsionless Dirac operator. We identify the group of twisted unitaries as the generator of torsion…

Mathematical Physics · Physics 2024-07-29 Pierre Martinetti , Gaston Nieuviarts , Ruben Zeitoun

Noncommutative geometry provides both a unified description of the Standard Model of particle physics together with Einstein-Hilbert action (in euclidean signature) and some tools to go beyond the Standard Model. In this paper, we extend to…

Mathematical Physics · Physics 2021-07-21 Manuele Filaci , Pierre Martinetti , Simone Pesco

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\in\Lambda^3M$ by means of twistor theory. An optimal lower bound for the first eigenvalue of the Dirac…

Differential Geometry · Mathematics 2013-11-05 Ilka Agricola , Julia Becker-Bender , Hwajeong Kim