Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra

Abstract

We study a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra. We find that the boundary dynamics is described by an enlargement and deformation of the bms 3 algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the super-translations in the standard bms 3 algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions of standard asymptotically flat case. The field content of the theory is different than the one of General Relativity, but it includes all its geometries as particular solutions. In this line, we also study the stationary solutions of the theory in ADM form and we show that the vacuum energy and the vacuum angular momentum of the stationary configuration are influenced by the presence of the gravitational Maxwell field.

Three-dimensional Maxwellian extended Bargmann supergravity

“…where J A are the spacetime rotations, P A the spacetime translations, and Z A are new generators characterized and introduced in [36,37] (A = 0, 1, 2 and η AB = diag(−, +, +)). A gauge-invariant CS gravity action in three (meaning 2+1, here as well as in the sequel) dimensions based on the above written Maxwell algebra has been constructed in [44][45][46]71]. The CS action is constructed using the connection one-form A = A A T A taking values in the Maxwell algebra generated by {J A , P A , Z A }, that is…”

“…More recently, a Maxwell CS formulation in three spacetime dimensions has been explored in [44]. Its solution [45,46], generalization to higher spin [47], and asymptotic symmetry [46,48] have been subsequently studied by diverse authors.…”

On stabilization of Maxwell-BMS algebra

“…Such infinite-dimensional symmetry algebra in presence of three central terms can also be obtained through the semi-group expansion method [31]. This algebra describes the asymptotic symmetry of a three-dimensional Chern-Simons gravity theory invariant under the Maxwell algebra [78]. Interestingly, the central charges c JJ , c JP and c JM can be related to three terms of the Chern-Simons Maxwell gravity action as follows [78]:…”

Three-dimensional exotic Newtonian gravity with cosmological constant

“…Indeed, it would be interesting to study the construction of a Maxwellian version of the extended Newtonian algebra [work in progress]. The Maxwell algebra, introduced in [54,55], have been of recent interest in the (super)gravity context [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Its non-relativistic version has been explored in [73] and subsequently recovered from an enlarged extended Bargmann algebra [49].…”