Boundary Heisenberg Algebras and Their Deformations
| Title: | Boundary Heisenberg Algebras and Their Deformations |
|---|---|
| Authors: | Enriquez-Rojo, Martin, Safari, H. R. |
| Publication Year: | 2021 |
| Collection: | Mathematics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| Subject Terms: | High Energy Physics - Theory, General Relativity and Quantum Cosmology, Mathematical Physics |
| More Details: | We investigate the deformations and rigidity of boundary Heisenberg-like algebras. In particular, we focus on the Heisenberg and $\text{Heisenberg}\oplus\mathfrak{witt}$ 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 $\text{Heisenberg}\oplus\mathfrak{witt}$ and the asymptotic symmetry algebra Weyl-$\mathfrak{bms}_3$ are not connected via single deformation but in a more subtle way. Comment: 28+19 pages and 1 diagram. V2 includes a new appendix on theory of deformations and enlarged discussions |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2111.13225 |
| Accession Number: | edsarx.2111.13225 |
| Database: | arXiv |
| Description not available. |