190 research outputs found
Fermions and Supersymmetry in Exceptional Field Theory
We construct the supersymmetric completion of E-covariant
exceptional field theory. The theory is based on a -dimensional
generalized space-time subject to a covariant section constraint. The fermions
are tensors under the local Lorentz group
and transform as weighted scalars under the E (internal) generalized
diffeomorphisms. We present the complete Lagrangian and prove its invariance
under supersymmetry. Upon explicit solution of the section constraint the
theory embeds full supergravity and IIB supergravity, respectively.Comment: 23 pages + Appendi
Rigid supersymmetric theories in 4d Riemannian space
We consider rigid supersymmetric theories in four-dimensional Riemannian spin
manifolds. We build the Lagrangian directly in Euclidean signature from the
outset, keeping track of potential boundary terms. We reformulate the
conditions for supersymmetry as a set of conditions on the torsion classes of a
suitable SU(2) or trivial G-structure. We illustrate the formalism with a
number of examples including supersymmetric backgrounds with non-vanishing Weyl
tensor.Comment: 26 page
SO(9) supergravity in two dimensions
We present maximal supergravity in two dimensions with gauge group SO(9). The
construction is based on selecting the proper embedding of the gauge group into
the infinite-dimensional symmetry group of the ungauged theory. The bosonic
part of the Lagrangian is given by a (dilaton-)gravity coupled non-linear
gauged sigma-model with Wess-Zumino term. We give explicit expressions for the
fermionic sector, the Yukawa couplings and the scalar potential which supports
a half-supersymmetric domain wall solution. The theory is expected to describe
the low-energy effective action upon reduction on the D0-brane near-horizon
warped AdS_2 x S^8 geometry, dual to the supersymmetric (BFSS) matrix quantum
mechanics.Comment: 35 pages, 1 figur
Exceptional Field Theory II: E
We introduce exceptional field theory for the group E_{7(7)}, based on a
(4+56)-dimensional spacetime subject to a covariant section condition. The
`internal' generalized diffeomorphisms of the coordinates in the fundamental
representation of E_{7(7)} are governed by a covariant `E-bracket', which is
gauged by 56 vector fields. We construct the complete and unique set of field
equations that is gauge invariant under generalized diffeomorphisms in the
internal and external coordinates. Among them feature the non-abelian twisted
self-duality equations for the 56 gauge vectors. We discuss the explicit
solutions of the section condition describing the embedding of the full,
untruncated 11-dimensional and type IIB supergravity, respectively. As a new
feature compared to the previously constructed E_{6(6)} formulation, some
components among the 56 gauge vectors descend from the 11-dimensional dual
graviton but nevertheless allow for a consistent coupling by virtue of a
covariantly constrained compensating 2-form gauge field.Comment: 24 pages, v2: version published in PR
E Exceptional Field Theory: Geometry, Fermions and Supersymmetry
We present the supersymmetric extension of the recently constructed
E exceptional field theory -- the manifestly U-duality covariant
formulation of the untruncated ten- and eleven-dimensional supergravities. This
theory is formulated on a (3+248) dimensional spacetime (modulo section
constraint) in which the extended coordinates transform in the adjoint
representation of E. All bosonic fields are E tensors and
transform under internal generalized diffeomorphisms. The fermions are tensors
under the generalized Lorentz group SO(1,2)SO(16), where SO(16) is the
maximal compact subgroup of E. Vanishing generalized torsion
determines the corresponding spin connections to the extent they are required
to formulate the field equations and supersymmetry transformation laws. We
determine the supersymmetry transformations for all bosonic and fermionic
fields such that they consistently close into generalized diffeomorphisms. In
particular, the covariantly constrained gauge vectors of E exceptional
field theory combine with the standard supergravity fields into a single
supermultiplet. We give the complete extended Lagrangian and show its
invariance under supersymmetry. Upon solution of the section constraint the
theory reduces to full D=11 or type IIB supergravity.Comment: 25 page
U-duality covariant gravity
We extend the techniques of double field theory to more general gravity
theories and U-duality symmetries, having in mind applications to the complete
D=11 supergravity. In this paper we work out a (3+3)-dimensional `U-duality
covariantization' of D=4 Einstein gravity, in which the Ehlers group SL(2,R) is
realized geometrically, acting in the 3 representation on half of the
coordinates. We include the full (2+1)-dimensional metric, while the `internal
vielbein' is a coset representative of SL(2,R)/SO(2) and transforms under gauge
transformations via generalized Lie derivatives. In addition, we introduce a
gauge connection of the `C-bracket', and a gauge connection of SL(2,R), albeit
subject to constraints. The action takes the form of (2+1)-dimensional gravity
coupled to a Chern-Simons-matter theory but encodes the complete D=4 Einstein
gravity. We comment on generalizations, such as an `
covariantization' of M-theory.Comment: 36 pages, v2: refs. added, to appear in JHE
Twin Supergravities
We study the phenomenon that pairs of supergravities can have identical
bosonic field content but different fermionic extensions. Such twin theories
are classified and shown to originate as truncations of a common theory with
more supersymmetry. Moreover, we discuss the possible gaugings and scalar
potentials of twin theories. This allows to pinpoint to which extent these
structures are determined by the purely bosonic structure of the underlying
Kac-Moody algebras and where supersymmetry comes to plays its role. As an
example, we analyze the gaugings of the six-dimensional N=(0,1) and N=(2,1)
theories with identical bosonic sector and explicitly work out their scalar
potentials. The discrepancy between the potentials finds a natural explanation
within maximal supergravity, in which both theories may be embedded.Comment: 27 pages. v2: ref added, published versio
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