950 research outputs found
Decomposition of some pointed Hopf algebras given by the canonical Nakayama automorphism
Every finite dimensional Hopf algebra is a Frobenius algebra, with Frobenius
homomorphism given by an integral. The Nakayama automorphism determined by it
yields a decomposition with degrees in a cyclic group. For a family of pointed
Hopf algebras, we determine necessary and sufficient conditions for this
decomposition to be strongly graded.Comment: 8 page
NS-NS fluxes in Hitchin's generalized geometry
The standard notion of NS-NS 3-form flux is lifted to Hitchin's generalized
geometry. This generalized flux is given in terms of an integral of a modified
Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the
generalized flux in a number of familiar examples, we show that it can compute
three-form flux, geometric flux and non-geometric Q-flux. Finally, a
generalized connection that acts on generalized vectors is described and we
show how the flux arises from it.Comment: 21 pages, 1 figure; v3: minor change
M-theory moduli spaces and torsion-free structures
Motivated by the description of M-theory compactifications to
four-dimensions given by Exceptional Generalized Geometry, we propose a way to
geometrize the M-theory fluxes by appropriately relating the compactification
space to a higher-dimensional manifold equipped with a torsion-free structure.
As a non-trivial example of this proposal, we construct a bijection from the
set of -structures on an eight-dimensional -bundle to the set
of -structures on the base space, fully characterizing the
-torsion clases when the total space is equipped with a torsion-free
-structure. Finally, we elaborate on how the higher-dimensional
manifold and its moduli space of torsion-free structures can be used to obtain
information about the moduli space of M-theory compactifications.Comment: 24 pages. Typos fixed. Minor clarifications adde
Extended geometry and gauged maximal supergravity
We consider generalized diffeomorphisms on an extended mega-space associated
to the U-duality group of gauged maximal supergravity in four dimensions, E_7.
Through the bein for the extended metric we derive dynamical (field-dependent)
fluxes taking values in the representations allowed by supersymmetry, and
obtain their quadratic constraints from gauge consistency conditions. A
covariant generalized Ricci tensor is introduced, defined in terms of a
connection for the generalized diffeomorphisms. We show that for any
torsionless and metric-compatible generalized connection, the Ricci scalar
reproduces the scalar potential of gauged maximal supergravity. We comment on
how these results extend to other groups and dimensions.Comment: 41 pages. v2,v3: minor changes and references adde
The gauge structure of Exceptional Field Theories and the tensor hierarchy
We address the construction of manifest U-duality invariant generalized
diffeomorphisms. The closure of the algebra requires an extension of the
tangent space to include a tensor hierarchy indicating the existence of an
underlying unifying structure, compatible with E_{11} and Borcherds algebras
constructions. We begin with four-dimensional gauged maximal supergravity, and
build a generalized Lie derivative that encodes all the gauge transformations
of the theory. A generalized frame is introduced, which accommodates for all
the degrees of freedom, including the tensor hierarchy. The generalized Lie
derivative defines generalized field-dependent fluxes containing all the
covariant quantities in the theory, and the closure conditions give rise to
their corresponding Bianchi Identities. We then move towards the construction
of a full generalized Lie derivative defined on an extended space, analyze the
closure conditions, and explore the connection with that of maximal gauged
supergravity via a generalized Scherk-Schwarz reduction, and with
11-dimensional supergravity.Comment: 53 page
AdS Vacua, Attractor Mechanism and Generalized Geometries
We consider flux vacua attractor equations in type IIA string theory
compactified on generalized geometries with orientifold projections. The
four-dimensional N=1 superpotential in this compactification can be written as
the sum of the Ramond-Ramond superpotential and a term described by
(non)geometric flux charges. We exhibit a simple model in which supersymmetric
AdS and Minkowski solutions are classified by means of discriminants of the two
superpotentials. We further study various configurations without Ramond-Ramond
flux charges. In this case we find supersymmetric AdS vacua both in the case of
compactifications on generalized geometries with SU(3) x SU(3) structures and
on manifolds with an SU(3)-structure without nongeometric flux charges. In the
latter case, we have to introduce correction terms into the prepotential in
order to realize consistent vacua.Comment: 35 pages, accepted version in JHE
Heterotic type IIA duality with fluxes - towards the complete story
In this paper we study the heterotic type IIA duality when fluxes are turned
on. We show that many of the known fluxes are dual to each other and claim that
certain fluxes on the heterotic side require that the type IIA picture is
lifted to M or even F-theory compactifications with geometric fluxes.Comment: 31 pages, references adde
Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
We consider compactifications of type II string theory on general SU(3) x
SU(3) structure backgrounds allowing for a very large set of fluxes, possibly
nongeometric ones. We study the effective 4d low energy theory which is a
gauged N=2 supergravity, and discuss how its data are obtained from the
formalism of the generalized geometry on T+T*. In particular we relate
Hitchin's special Kaehler metrics on the spaces of even and odd pure spinors to
the metric on the supergravity moduli space of internal metric and B-field
fluctuations. We derive the N=1 vacuum conditions from this N=2 effective
action, as well as from its N=1 truncation. We prove a direct correspondence
between these conditions and an integrated version of the pure spinor equations
characterizing the N=1 backgrounds at the ten dimensional level.Comment: 54 pages. v2, v3: minor change
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