On stabilization of Maxwell-BMS algebra

Abstract

In this work we present different infinite dimensional algebras which appear as deformations of the asymptotic symmetry of the three-dimensional Chern-Simons gravity for the Maxwell algebra. We study rigidity and stability of the infinite dimensional enhancement of the Maxwell algebra. In particular, we show that three copies of the Witt algebra and the bms 3 ⊕ witt algebra are obtained by deforming its ideal part. New family of infinite dimensional algebras are obtained by considering deformations of the other commutators which we have denoted as M(a, b; c, d) and M(ᾱ,β;ν). Interestingly, for the specific values a = c = d = 0, b = − 1 2 the obtained algebra M(0, − 1 2 ; 0, 0) corresponds to the twisted Schrödinger-Virasoro algebra. The central extensions of our results are also explored. The physical implications and relevance of the deformed algebras introduced here are discussed along the work.

Asymptotic symmetries of Maxwell Chern–Simons gravity with torsion

“…It is shown in [69] that the Maxwell algebra can be deformed into two different algebras: so(2, 2) ⊕ so(2, 1) and iso(2, 1) ⊕ so(2, 1). The former has been largely studied in [31,44,70,71] whose asymptotic symmetry is described by three copies of the Virasoro algebra [31,32], while the latter has only been approached through a deformation process [66,69]. In the present work, using the basis {J a , P a , M a }, we find asymptotic symmetry of the CS gravity theory based on the iso(2, 1) ⊕ so(2, 1) algebra.…”

“…In particular, by considering suitable boundary conditions, we show that the asymptotic symmetry can be written as the bms 3 ⊕ vir algebra. This infinite-dimensional symmetry was recently obtained as a deformation of the infinite-dimensional enhancement of the Maxwell algebra, denoted as Max 3 algebra [66]. We also show that the vanishing cosmological constant limit → ∞ can be applied not only at the CS gravity theory level but also at the asymptotic algebra, leading to the Maxwell CS gravity and its respective asymptotic symmetry previously introduced in [29].…”

“…Indeed, considering In this work, we analyze the consequences of this particular deformation of the Maxwell symmetry at the level of the asymptotic structure. In the Maxwell case, as was shown in [29], the presence of the additional gauge field f a leads to new effects compared to GR and the asymptotic symmetries is found to be a deformed bms 3 , denoted as Max 3 in [66]. Here, we explore the implications of deforming the Maxwell algebra as in (2.1).…”

“…One can see that J a and P a are not the generators of a Poincaré subalgebra. However, as it is pointed out in [66], (2.1) can be rewritten as the iso(2, 1) ⊕ so(2, 1) algebra. This can be seen by a redefinition of the generators,…”

“…4 we discuss the obtained results and possible future developments. Notation We adopt the same notation as [30,66,67] for the algebras; for algebras we generically use "mathfrak" fonts, like vir, bms 3 and Max 3 . The centrally extended version of an algebra g will be denoted byĝ, e.g.…”