48 research outputs found
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- generators, corresponds to a subset of a contraction of two copies
of WB. Finally, we show how the Poincar\'e group can be extended with
half-integer spin generators for dimensions.Comment: 12 pages, no figures. Matches published versio
Asymptotic gauge symmetries and gauge-invariant Poincar\'e generators in higher spacetime dimensions
The asymptotic symmetries of electromagnetism in all higher spacetime
dimensions are extended, by incorporating consistently angle-dependent
gauge transformations with a linear growth in the radial coordinate at
spatial infinity. Finiteness of the symplectic structure and preservation of
the asymptotic conditions require to impose a set of strict parity conditions,
under the antipodal map of the -sphere, on the leading order fields at
infinity. Canonical generators of the asymptotic symmetries are obtained
through standard Hamiltonian methods. Remarkably, the theory endowed with this
set of asymptotic conditions turns out to be invariant under a six-fold set of
angle-dependent transformations, whose generators form a centrally
extended abelian algebra. The new charges generated by the
gauge parameter are found to be conjugate to those associated to the now
improper subleading transformations, while the standard gauge transformations are canonically conjugate to the subleading
transformations. This algebraic structure,
characterized by the presence of central charges, allows us to perform a
nonlinear redefinition of the Poincar\'e generators, that results in the
decoupling of all of the charges from the Poincar\'e algebra. Thus, the
mechanism previously used in to find gauge-invariant Poincar\'e
generators is shown to be a robust property of electromagnetism in all
spacetime dimensions .Comment: 25 pages, no figures. References added. Matches with published
versio
Asymptotic structure of supergravity in 3D: extended super-BMS and nonlinear energy bounds
The asymptotically flat structure of supergravity in
three spacetime dimensions is explored. The asymptotic symmetries are spanned
by an extension of the super-BMS algebra, with two independent
currents of electric and magnetic type. These currents are associated to
fields being even and odd under parity, respectively. Remarkably, although the
fields do not generate a backreaction on the metric, they provide
nontrivial Sugawara-like contributions to the BMS generators, and hence to
the energy and the angular momentum. The entropy of flat cosmological
spacetimes with fields then acquires a nontrivial dependence on the
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
charge, the energy becomes bounded from below by the energy of the
ground state shifted by the square of the electric-like 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
super-Virasoro algebra. Indeed, our super-BMS algebra can
be recovered from the flat limit of the superconformal algebra with
, 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
Simplifying (super-)BMS algebras
We show that the non-linear BMS symmetry algebra of asymptotically flat
Einstein gravity in five dimensions, as well as the super-BMS superalgebra
of asymptotically flat supergravity, can be redefined so as to take a direct
sum structure. In the new presentation of the (super-)algebra, angle-dependent
translations and angle-dependent supersymmetry transformations commute with the
(super-)Poincar\'e generators. We also explain in detail the structure and
charge-integrability of asymptotic symmetries with symmetry parameters
depending on the fields (through the charges themselves), a topic relevant for
nonlinear asymptotic symmetry algebras.Comment: 23 pages, no figure
A note on the asymptotic symmetries of electromagnetism
We extend the asymptotic symmetries of electromagnetism in order to
consistently include angle-dependent gauge transformations
that involve terms growing at spatial infinity linearly and logarithmically in
, . The charges of the logarithmic transformations are found to
be conjugate to those of the transformations (abelian algebra
with invertible central term) while those of the
transformations are conjugate to those of the subleading
transformations. Because of this structure, one can decouple the
angle-dependent asymptotic symmetry from the Poincar\'e algebra, just as
in the case of gravity: the generators of these internal transformations are
Lorentz scalars in the redefined algebra. This implies in particular that one
can give a definition of the angular momentum which is free from gauge
ambiguities. The change of generators that brings the asymptotic symmetry
algebra to a direct sum form involves non linear redefinitions of the charges.
Our analysis is Hamiltonian throughout and carried at spatial infinity.Comment: 25 pages, no figures. One note added and minor typos corrected.
Matches with published versio
Hypergravity in five dimensions
We show that a spin- field can be consistently coupled to gravitation
without cosmological constant in five-dimensional spacetimes. The fermionic
gauge "hypersymmetry" requires the presence of a finite number of additional
fields, including a couple of fields, a spinorial two-form, the dual of
the graviton (of mixed Young symmetry) and a spin- field. The
gravitational sector of the action is described by the purely quadratic
Gauss-Bonnet term, so that the field equations for the metric are of second
order. The local gauge symmetries of the full action principle close without
the need of auxiliary fields. The field content corresponds to the components
of a connection for an extension of the "hyper-Poincar\'e" algebra, which apart
from the Poincar\'e and spin- generators, includes a generator of spin
and a central extension. It is also shown that this algebra admits an
invariant trilinear form, which allows to formulate hypergravity as a gauge
theory described by a Chern-Simons action in five dimensions.Comment: 17 pages, no figures, minor changes, references adde
Logarithmic supertranslations and supertranslation-invariant Lorentz charges
We extend the BMS(4) group by adding logarithmic supertranslations. This is
done by relaxing the boundary conditions on the metric and its conjugate
momentum at spatial infinity in order to allow logarithmic terms of carefully
designed form in the asymptotic expansion, while still preserving finiteness of
the action. Standard theorems of the Hamiltonian formalism are used to derive
the (finite) generators of the logarithmic supertranslations. As the ordinary
supertranslations, these depend on a function of the angles. Ordinary and
logarithmic supertranslations are then shown to form an abelian subalgebra with
non-vanishing central extension. Because of this central term, one can make
nonlinear redefinitions of the generators of the algebra so that the pure
supertranslations ( in a spherical harmonic expansion) and the
logarithmic supertranslations have vanishing brackets with all the Poincar\'e
generators, and, in particular, transform in the trivial representation of the
Lorentz group. The symmetry algebra is then the direct sum of the Poincar\'e
algebra and the infinite-dimensional abelian algebra formed by the pure
supertranslations and the logarithmic supertranslations (with central
extension). The pure supertranslations are thus completely decoupled from the
standard Poincar\'e algebra in the asymptotic symmetry algebra. This implies in
particular that one can provide a definition of the angular momentum which is
manifestly free from supertranslation ambiguities. An intermediate redefinition
providing a partial decoupling of the pure and logarithmic supertranslations is
also given.Comment: 52 pages, no figures, one comment adde