Gauge theories on κ-Minkowski spaces: Twist and modular operators

Philippe Mathieu (1) , Jean-Christophe Wallet (2)

1 Department of Mathematics, University of Notre dame
2 IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie

We discuss the construction of κ-Poincaré invariant actions for gauge theories on κ-Minkowski spaces. We consider various classes of untwisted and (bi)twisted differential calculi. Starting from a natural class of noncommutative differential calculi based on a particular type of twisted derivations belonging to the algebra of deformed translations, combined with a twisted extension of the notion of connection, we prove an algebraic relation between the various twists and the classical dimension d of the κ-Minkowski space(-time) ensuring the gauge invariance of the candidate actions for gauge theories. We show that within a natural differential calculus based on a distinguished set of twisted derivations, d=5 is the unique value for the classical dimension at which the gauge action supports both the gauge invariance and the κ-Poincaré in-variance. Within standard (untwisted) differential calculi, we show that the full gauge invariance cannot be achieved, although an invariance under a group of transformations constrained by the modular (Tomita) operator stemming from the κ-Poincaré invariance still holds.

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Philippe Mathieu, Jean-Christophe Wallet. Gauge theories on κ-Minkowski spaces: Twist and modular operators. Journal of High Energy Physics, 2020, 05, pp.112. ⟨10.1007/JHEP05(2020)112⟩. ⟨hal-02474406v2⟩