Asymptotic structure of N=2\mathcal{N}=2 supergravity in 3D: extended super-BMS3_3 and nonlinear energy bounds

The asymptotically flat structure of $\mathcal{N}=(2,0)$ supergravity in three spacetime dimensions is explored. The asymptotic symmetries are spanned by an extension of the super-BMS$_3$ algebra, with two independent $\hat{u}(1)$ currents of electric and magnetic type. These currents are associated to $U(1)$ fields being even and odd under parity, respectively. Remarkably, although the $U(1)$ fields do not generate a backreaction on the metric, they provide nontrivial Sugawara-like contributions to the BMS$_3$ generators, and hence to the energy and the angular momentum. The entropy of flat cosmological spacetimes with $U(1)$ fields then acquires a nontrivial dependence on the $\hat{u}(1)$ charges. If the spin structure is odd, the ground state corresponds to Minkowski spacetime, and although the anticommutator of the canonical supercharges is linear in the energy and in the electric-like $\hat{u}(1)$ charge, the energy becomes bounded from below by the energy of the ground state shifted by the square of the electric-like $\hat{u}(1)$ charge. If the spin structure is even, the same bound for the energy generically holds, unless the absolute value of the electric-like charge is less than minus the mass of Minkowski spacetime in vacuum, so that the energy has to be nonnegative. The explicit form of the Killing spinors is found for a wide class of configurations that fulfills our boundary conditions, and they exist precisely when the corresponding bounds are saturated. It is also shown that the spectra with periodic or antiperiodic boundary conditions for the fermionic fields are related by spectral flow, in a similar way as it occurs for the $\mathcal{N}=2$ super-Virasoro algebra. Indeed, our super-BMS$_3$ algebra can be recovered from the flat limit of the superconformal algebra with $\mathcal{N}=(2,2)$, truncating the fermionic generators of the right copy.Comment: 32 pages, no figures. Talk given at the ESI Programme and Workshop "Quantum Physics and Gravity" hosted by ESI, Vienna, June 2017. V3: minor changes and typos corrected. Matches published versio

Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension

We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern--Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all carrollian, galilean, and aristotelian counterparts of the lorentzian theories. In order to define a nondegenerate bilinear form for each of the theories, we introduce (not necessarily central) extensions of the original kinematical algebras. Using the structure of so-called double extensions, this can be done systematically. For homogeneous spaces that arise as a limit of (anti-)de Sitter spacetime, we show that it is possible to take the limit on the level of the action, after an appropriate extension. We extend our systematic construction of nondegenerate bilinear forms also to all higher-dimensional kinematical algebras.Comment: 52 pages, 2 figures, 11 tables; v2: matches published version, additional references added and incorporated referee suggestion

Extension of the Poincar\'e group with half-integer spin generators: hypergravity and beyond

An extension of the Poincar\'e group with half-integer spin generators is explicitly constructed. We start discussing the case of three spacetime dimensions, and as an application, it is shown that hypergravity can be formulated so as to incorporate this structure as its local gauge symmetry. Since the algebra admits a nontrivial Casimir operator, the theory can be described in terms of gauge fields associated to the extension of the Poincar\'e group with a Chern-Simons action. The algebra is also shown to admit an infinite-dimensional non-linear extension, that in the case of fermionic spin-$3/2$ generators, corresponds to a subset of a contraction of two copies of WB$_2$. Finally, we show how the Poincar\'e group can be extended with half-integer spin generators for $d\geq3$ dimensions.Comment: 12 pages, no figures. Matches published versio

Asymptotic symmetries and dynamics of three-dimensional flat supergravity

A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a supersymmetric extension of the BMS$_3$ algebra with an appropriate central charge. The energy is manifestly bounded from below with the ground state given by the null orbifold or Minkowski spacetime for periodic, respectively antiperiodic boundary conditions on the gravitino. These results are related to the corresponding ones in AdS$_3$ supergravity by a suitable flat limit. The analysis is generalized to the case of minimal flat supergravity with additional parity odd terms for which the Poisson algebra of canonical generators form a representation of the super-BMS$_3$ algebra with an additional central charge.Comment: 13 pages, no figure

Revisiting the asymptotic dynamics of General Relativity on AdS3_3

The dual dynamics of Einstein gravity on AdS$_3$ supplemented with boundary conditions of KdV-type is identified. It corresponds to a two-dimensional field theory at the boundary, described by a novel action principle whose field equations are given by two copies of the "potential modified KdV equation". The asymptotic symmetries then transmute into the global Noether symmetries of the dual action, giving rise to an infinite set of commuting conserved charges, implying the integrability of the system. Noteworthy, the theory at the boundary is non-relativistic and possesses anisotropic scaling of Lifshitz type.Comment: 18 page

Enlarged super-bms3\mathfrak{bms}_{3} algebra and its flat limit

In this paper we analyze the asymptotic symmetries of the three-dimensional Chern-Simons supergravity for a supersymmetric extension of the semi-simple enlargement of the Poincar\'e algebra, also known as AdS-Lorentz superalgebra, which is characterized by two fermionic generators. We propose a consistent set of asymptotic boundary conditions for the aforementioned supergravity theory, and we show that the corresponding charge algebra defines a supersymmetric extension of the semi-simple enlargement of the $\mathfrak{bms}_{3}$ algebra, with three independent central charges. This asymptotic symmetry algebra can alternatively be written as the direct sum of three copies of the Virasoro algebra, two of which are augmented by supersymmetry. Interestingly, we show that the flat limit of the obtained asymptotic algebra corresponds to a deformed super-$\mathfrak{bms}_{3}$ algebra, being the charge algebra of the minimal Maxwell supergravity theory in three dimensions.Comment: 17 page

Singular limits of spacetimes and their isometries

We consider spacetime metrics with a given (but quite generic) dependence on a dimensionful parameter such that in the 0 and infinity limits of that parameter the metric becomes singular. We study the isometry groups of the original spacetime metrics and of the singular metrics that arise in the limits and the corresponding symmetries of the motion of p-branes evolving in them, showing how the Killing vectors and their Lie algebras can be found in general. We illustrate our general results with several examples which include limits of anti-de Sitter spacetime in which the holographic screen is one of the singular metrics and of pp-waves.Comment: Latex2e paper, 48 page