Boundary Heisenberg algebras and their deformations

Enriquez Rojo, Martin and Safari, H. R. (2022): Boundary Heisenberg algebras and their deformations. In: Journal of High Energy Physics, No. 3

Abstract

We investigate the deformations and rigidity of boundary Heisenberg-like algebras. In particular, we focus on the Heisenberg and Heisenberg circle plus mitt algebras which arise as symmetry algebras in three-dimensional gravity theories. As a result of the deformation procedure we find a large class of algebras. While some of these algebras are new, some of them have already been obtained as asymptotic and boundary symmetry algebras, supporting the idea that symmetry algebras associated to diverse boundary conditions and spacetime loci are algebraically interconnected through deformation of algebras. The deformation/contraction relationships between the new algebras are investigated. In addition, it is also shown that the deformation procedure reaches new algebras inaccessible to the Sugawara construction. As a byproduct of our analysis, we obtain that Heisenberg circle plus mitt and the asymptotic symmetry algebra Weyl-bms(3) are not connected via single deformation but in a more subtle way.

• Item Type: Journal article
• Faculties: Physics
• Subjects: 500 Science > 530 Physics
• ISSN: 1029-8479
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 491502892