3,875 research outputs found
Uniqueness of and pure supergravities in 4D
After proving the impossibility of consistent non-minimal coupling of a real
Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of
introducing the graviton in order to couple a complex Rarita-Schwinger gauge
field to electromagnetism, with or without a cosmological term, thereby
obtaining pure supergravity as the only possibility. These results
are obtained with the BRST-BV deformation method around the flat and (A)dS
backgrounds in 4 dimensions. The same method applied to vectors, real spin-3/2 gauge fields and at most one real spinor field also requires
gravity and yields pure supergravity as well as pure
supergravity coupled to a vector supermultiplet, with or without cosmological
terms. Independently from the matter content, we finally derive strong
necessary quadratic constraints on the possible gaugings for an arbitrary
number of spin-1 and spin-3/2 gauge fields, that are relevant for larger
supergravities.Comment: LaTeX, 31 + 1 pages, no figure. v2: Extended discussion at the end of
Section 3, corrected typos and references adde
, Borcherds algebras and maximal supergravity
The dynamical -forms of torus reductions of maximal supergravity theory
have been shown some time ago to possess remarkable algebraic structures. The
set ("dynamical spectrum") of propagating -forms has been described as a
(truncation of a) real Borcherds superalgebra \mf{V}_D that is characterized
concisely by a Cartan matrix which has been constructed explicitly for each
spacetime dimension In the equations of motion, each
differential form of degree is the coefficient of a (super-) group
generator, which is itself of degree for a specific gradation (the
\mf{V}-gradation). A slightly milder truncation of the Borcherds superalgebra
enables one to predict also the "spectrum" of the non-dynamical and
-forms. The maximal supergravity -form spectra were reanalyzed more
recently by truncation of the field spectrum of to the -forms that
are relevant after reduction from 11 to dimensions. We show in this paper
how the Borcherds description can be systematically derived from the split
("maximally non compact") real form of for This explains
not only why both structures lead to the same propagating -forms and their
duals for but also why one obtains the same -forms
and "top" -forms. The Borcherds symmetries \mf{V}_2 and \mf{V}_1 are new
too. We also introduce and use the concept of a presentation of a Lie algebra
that is covariant under a given subalgebra.Comment: 39 pages. Version 2 contains improved presentation in particular an
extra appendix B giving details on the infinite rank limit possibility.
Version to appear in JHE
Counterterms in type I Supergravities
We compute the one-loop divergences of D=10, N=1 supergravity and of its
reduction to D=8. We study the tensor structure of the counterterms appearing
in D=8 and D=10 and compare these to expressions previously found in the low
energy expansion of string theory. The infinities have the primitive Yang-Mills
tree amplitude as a common factor.Comment: 26 pages, Latex, 4 eps figure
Cosmological billiards and oxidation
We show how the properties of the cosmological billiards provide useful
information (spacetime dimension and -form spectrum) on the oxidation
endpoint of the oxidation sequence of gravitational theories. We compare this
approach to the other available methods: subgroups and the
superalgebras of dualities.Comment: To appear in the Proceedings of the 27th Johns Hopkins Workshop and
in the Proceedings of the 36th International Symposium Ahrenshoop; v2: minor
error correcte
Gravitational duality near de Sitter space
Gravitational instantons ''Lambda-instantons'' are defined here for any given
value Lambda of the cosmological constant. A multiple of the Euler
characteristic appears as an upper bound for the de Sitter action and as a
lower bound for a family of quadratic actions. The de Sitter action itself is
found to be equivalent to a simple and natural quadratic action. In this paper
we also describe explicitly the reparameterization and duality invariances of
gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant
doubling of the fields using the Hamiltonian formalism leads to first order
time evolution with manifest duality symmetry. As a special case we recover the
linear flat space result of Henneaux and Teitelboim by a smooth limiting
process.Comment: 13 pages, no figure - v2 contains only small redactional changes (one
reference added) and is essentially the published versio
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