30 research outputs found
Kac-Moody and Borcherds Symmetries of Six-Dimensional Chiral Supergravity
We investigate the conjectured infinite-dimensional hidden symmetries of
six-dimensional chiral supergravity coupled to two vector multiplets and two
tensor multiplets, which is known to possess the symmetry upon
dimensional reduction to three spacetime dimensions. Two things are done. (i)
First, we analyze the geodesic equations on the coset space
using the level decomposition associated with
the subalgebra of and
show their equivalence with the bosonic equations of motion of six-dimensional
chiral supergravity up to the level where the dual graviton appears. In
particular, the self-duality condition on the chiral -form is automatically
implemented in the sense that no dual potential appears for that -form, in
contradistinction with what occurs for the non chiral -forms. (ii) Second,
we describe the -form hierarchy of the model in terms of its -duality
Borcherds superalgebra, of which we compute the Cartan matrix.Comment: 31 pages. v2: Error in section 6.3 corrected, Dynkin diagram now
appears correctly, minor typo
Aspects of electric-magnetic dualities in maximal supergravity
This thesis is devoted to various aspects of electric-magnetic duality and
its gravitational generalization, with an emphasis on the case of maximal
supergravity. It is divided into three parts. In the first part, we review the
the Cremmer-Julia "hidden" symmetries of maximal supergravity in various
dimensions. Two new results are obtained: we prove that those symmetries appear
if and only if the Chern-Simons coupling of the theory takes the value
predicted by supersymmetry, and we obtain a manifestly -invariant
formula for the entropy of non-extremal black holes in ,
supergravity. The second part is motivated by supergravity gaugings. We examine
through BRST methods the local deformations of non-minimally coupled scalars
and abelian vector fields in four dimensions. We prove that they are all of the
usual Yang-Mills type, i.e., correspond to the gauging of some rigid symmetries
of the undeformed theory. We also show that other Lagragians considered in the
literature, containing additional fields, do not allow for gaugings that cannot
be reached starting from the usual Lagrangian. In the third part, we construct
self-contained action principles for several self-dual free fields in six
dimensions. These fields are motivated by two considerations: they allow for a
geometric interpretation of the electric-magnetic duality symmetries of
linearized gravity in four dimensions, and they also appear in the spectrum of
the chiral and "exotic supergravities" in place of a
metric. The free action and supersymmetry transformations for those theories
are then explicitly constructed. We check that they reduce to linearized
maximal supergravity in five dimensions, and also generalize previous works on
linearized supergravity by other authors in which the graviton and its dual
appear on the same footing at the level of the action.Comment: Ph.D. Thesis, Universit\'e Libre de Bruxelles. 139 pages +
appendices. Based on arXiv:1505.07355, arXiv:1510.03582, arXiv:1612.02772,
arXiv:1709.06014, arXiv:1711.07448, arXiv:1712.08126, arXiv:1804.06729 and
arXiv:1804.1012
Enhancement of hidden symmetries and Chern-Simons couplings
We study the role of Chern--Simons couplings for the appearance of enhanced
symmetries of Cremmer--Julia type in various theories. It is shown explicitly
that for generic values of the Chern--Simons coupling there is only a parabolic
Lie subgroup of symmetries after reduction to three space-time dimensions but
that this parabolic Lie group gets enhanced to the full and larger
Cremmer--Julia Lie group of hidden symmetries if the coupling takes a specific
value. This is heralded by an enhanced isotropy group of the metric on the
scalar manifold. Examples of this phenomenon are discussed as well as the
relation to supersymmetry. Our results are also connected with rigidity
theorems of Borel-like algebras.Comment: To appear in the Proceedings of the 9th Workshop and School on
"Quantum Field Theory and Hamiltonian Systems", 24-28 September 2014, Sinaia,
Romani
Higher spins from exotic dualisations
At the free level, a given massless field can be described by an infinite
number of different potentials related to each other by dualities. In terms of
Young tableaux, dualities replace any number of columns of height by
columns of height , where is the spacetime dimension: in
particular, applying this operation to empty columns gives rise to potentials
containing an arbitrary number of groups of extra antisymmetric indices.
Using the method of parent actions, action principles including these
potentials, but also extra fields, can be derived from the usual ones. In this
paper, we revisit this off-shell duality and clarify the counting of degrees of
freedom and the role of the extra fields. Among others, we consider the
examples of the double dual graviton in and two cases, one topological
and one dynamical, of exotic dualities leading to spin three fields in .Comment: 31 pages. v2: typos corrected, published versio
Prepotentials for linearized supergravity
Linearized supergravity in arbitrary dimension is reformulated into a first
order formalism which treats the graviton and its dual on the same footing at
the level of the action. This generalizes previous work by other authors in two
directions: 1) we work in arbitrary space-time dimension, and 2) the gravitino
field and supersymmetry are also considered. This requires the construction of
conformally invariant curvatures (the Cotton fields) for a family of mixed
symmetry tensors and tensor-spinors, whose properties we prove (invariance;
completeness; conformal Poincar\'e lemma). We use these geometric tools to
solve the Hamiltonian constraints appearing in the first order formalism of the
graviton and gravitino: the constraints are solved through the introduction of
prepotentials enjoying (linearized) conformal invariance. These new variables
(two tensor fields for the graviton, one tensor-spinor for the gravitino) are
injected into the action and equations of motion, which take a geometrically
simple form in terms of the Cotton tensor(-spinors) of the prepotentials. In
particular, the equations of motion of the graviton are equivalent to twisted
self-duality conditions. We express the supersymmetric transformations of the
graviton and gravitino into each other in terms of the prepotentials. We also
reproduce the dimensional reduction of supergravity within the prepotential
formalism. Finally, our formulas in dimension five are recovered from the
dimensional reduction of the already known prepotential formulation of the
six-dimensional maximally supersymmetric theory.Comment: v2: updated reference
Gravitational anomalies of fermionic higher-spin fields
Using the Atiyah-Singer index theorem, we formally compute gravitational
anomalies for fermionic higher-spin fields in two, six and ten dimensions, as
well as the U(1) mixed gauge-gravitational anomaly in four dimensions. In all
cases, anomaly cancellations are found for an infinite tower of fields with
alternating chiralities.Comment: 11 pages. v2: Comments and references added, published versio
Deformations of vector-scalar models
Abelian vector fields non-minimally coupled to uncharged scalar fields arise
in many contexts. We investigate here through algebraic methods their
consistent deformations ("gaugings"), i.e., the deformations that preserve the
number (but not necessarily the form or the algebra) of the gauge symmetries.
Infinitesimal consistent deformations are given by the BRST cohomology classes
at ghost number zero. We parametrize explicitly these classes in terms of
various types of global symmetries and corresponding Noether currents through
the characteristic cohomology related to antifields and equations of motion.
The analysis applies to all ghost numbers and not just ghost number zero. We
also provide a systematic discussion of the linear and quadratic constraints on
these parameters that follow from higher-order consistency. Our work is
relevant to the gaugings of extended supergravities.Comment: v2: references added, typos corrected, minor changes for clarit
Homotopy Transfer and Effective Field Theory II: Strings and Double Field Theory
We continue our study of effective field theory via homotopy transfer of
-algebras, and apply it to tree-level non-Wilsonian effective actions
of the kind discussed by Sen in which the modes integrated out are comparable
in mass to the modes that are kept. We focus on the construction of effective
actions for string states at fixed levels and in particular on the construction
of weakly constrained double field theory. With these examples in mind, we
discuss closed string theory on toroidal backgrounds and resolve some subtle
issues involving vertex operators, including the proper form of cocycle factors
and of the reflector state. This resolves outstanding issues concerning the
construction of covariant closed string field theory on toroidal backgrounds.
The weakly constrained double field theory is formally obtained from closed
string field theory on a toroidal background by integrating out all but the
doubly massless' states and homotopy transfer then gives a prescription for
determining the theory's vertices and symmetries. We also discuss consistent
truncation in the context of homotopy transfer.Comment: 53 pages. v2: References adde