18 research outputs found
On conformal higher spin wave operators
We analyze free conformal higher spin actions and the corresponding wave
operators in arbitrary even dimensions and backgrounds. We show that the wave
operators do not factorize in general, and identify the Weyl tensor and its
derivatives as the obstruction to factorization. We give a manifestly
factorized form for them on (A)dS backgrounds for arbitrary spin and on
Einstein backgrounds for spin 2. We are also able to fix the conformal wave
operator in d=4 for s=3 up to linear order in the Riemann tensor on generic
Bach-flat backgrounds.Comment: 26 pages, includes Mathematica notebook. Version published in JHE
Polycritical Gravities
We present higher-derivative gravities that propagate an arbitrary number of
gravitons of different mass on (A)dS backgrounds. These theories have multiple
critical points, at which the masses degenerate and the graviton energies are
non-negative. For six derivatives and higher there are critical points with
positive energy.Comment: Version to be publishe
On unitary subsectors of polycritical gravities
We study higher-derivative gravity theories in arbitrary space-time dimension
d with a cosmological constant at their maximally critical points where the
masses of all linearized perturbations vanish. These theories have been
conjectured to be dual to logarithmic conformal field theories in the
(d-1)-dimensional boundary of an AdS solution. We determine the structure of
the linearized perturbations and their boundary fall-off behaviour. The
linearized modes exhibit the expected Jordan block structure and their inner
products are shown to be those of a non-unitary theory. We demonstrate the
existence of consistent unitary truncations of the polycritical gravity theory
at the linearized level for odd rank.Comment: 22 pages. Added references, rephrased introduction slightly.
Published versio
A Note on E11 and Three-dimensional Gauged Supergravity
We determine the gauge symmetries of all p-forms in maximal three-dimensional
gauged supergravity by requiring invariance of the Lagrangian. It is shown that
in a particular ungauged limit these symmetries are in precise correspondence
to those predicted by the very-extended Kac-Moody algebra E11. We demonstrate
that whereas in the ungauged limit the bosonic gauge algebra closes off-shell,
the closure is only on-shell in the full gauged theory. This underlines the
importance of dynamics for understanding the Kac-Moody origin of the symmetries
of gauged supergravity.Comment: Published versio
E10 and Gauged Maximal Supergravity
We compare the dynamics of maximal three-dimensional gauged supergravity in
appropriate truncations with the equations of motion that follow from a
one-dimensional E10/K(E10) coset model at the first few levels. The constant
embedding tensor, which describes gauge deformations and also constitutes an
M-theoretic degree of freedom beyond eleven-dimensional supergravity, arises
naturally as an integration constant of the geodesic model. In a detailed
analysis, we find complete agreement at the lowest levels. At higher levels
there appear mismatches, as in previous studies. We discuss the origin of these
mismatches.Comment: 34 pages. v2: added references and typos corrected. Published versio
Kac-Moody Spectrum of (Half-)Maximal Supergravities
We establish the correspondence between, on one side, the possible gaugings
and massive deformations of half-maximal supergravity coupled to vector
multiplets and, on the other side, certain generators of the associated very
extended Kac-Moody algebras. The difference between generators associated to
gaugings and to massive deformations is pointed out. Furthermore, we argue that
another set of generators are related to the so-called quadratic constraints of
the embedding tensor. Special emphasis is placed on a truncation of the
Kac-Moody algebra that is related to the bosonic gauge transformations of
supergravity. We give a separate discussion of this truncation when non-zero
deformations are present. The new insights are also illustrated in the context
of maximal supergravity.Comment: Added references, published versio
Kac-Moody symmetries and gauged supergravity
Symmetry. Not only makes it our world round, but it's also what makes it go round. From the perfect circular wheels on our bikes and cars that deliver an enjoyable ride, to the error-correction protocols that keep e-mails from turning into junk; it's literally all around us. It's also symmetry that dictates the laws of nature. On the small scale the symmetry group of the Standard Model controls the interactions in molecules, atoms, and nuclei. On the large scale gravity is governed by Einstein's symmetry principle of our space-time.
This thesis deals with a certain class of symmetries known as Kac-Moody algebras. In contrast to the symmetries of the Standard Model and gravity, Kac-Moody algebras are infinite. They appear in the context of M-theory, an as of yet unknown theory that might both describe the Standard Model and gravity. In this thesis we will show how Kac-Moody algebras unify all the low-energy limits of M-theory, which are known as supergravities. Moreover, the Kac-Moody algebras contain information that corresponds exactly to all the known gauge deformations of these supergravities. We will demonstrate how to obtain the field content of the various gauged supergravities from Kac-Moody algebras, and attempt to relate the equations of motion of both sides to each other.