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Paper   IPM / Physic / 16842
School of Physics
  Title:   Boundary Heisenberg Algebras and Their Deformations
1.  M.E. Rojo
2.  H.R. Safari
  Status:   Published
  Journal: JHEP
  Vol.:  03
  Year:  2022
  Pages:   089
  Supported by:  IPM
We investigate the deformations and rigidity of boundary Heisenberg-like algebras. In particular, we focus on the Heisenberg and Heisenberg+Witt algebras which arise as symmetry algebras in three-dimensional gravity theories. Their deformations include multiple asymptotic and boundary symmetry algebras previously obtained in the literature, supporting the idea that symmetry algebras associated to diverse boundary conditions and spacetime loci are algebraically interconnected. 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+Witt and the asymptotic symmetry algebra Weyl-bms_3 are not connected via single deformation but in a more subtle way.

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