903 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
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
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
New families of interpolating type IIB backgrounds
We construct new families of interpolating two-parameter solutions of type
IIB supergravity. These correspond to D3-D5 systems on non-compact
six-dimensional manifolds which are T^2 fibrations over Eguchi-Hanson and
multi-center Taub-NUT spaces, respectively. One end of the interpolation
corresponds to a solution with only D5 branes and vanishing NS three-form flux.
A topology changing transition occurs at the other end, where the internal
space becomes a direct product of the four-dimensional surface and the
two-torus and the complexified NS-RR three-form flux becomes imaginary
self-dual. Depending on the choice of the connections on the torus fibre, the
interpolating family has either N=2 or N=1 supersymmetry. In the N=2 case it
can be shown that the solutions are regular.Comment: 20 page
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
Numerically flat Higgs vector bundles
After providing a suitable definition of numerical effectiveness for Higgs
bundles, and a related notion of numerical flatness, in this paper we prove,
together with some side results, that all Chern classes of a Higgs-numerically
flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if
and only if it is has a filtration whose quotients are flat stable Higgs
bundles. We also study the relation between these numerical properties of Higgs
bundles and (semi)stability.Comment: 11 page
Nongeometry, Duality Twists, and the Worldsheet
In this paper, we use orbifold methods to construct nongeometric backgrounds,
and argue that they correspond to the spacetimes discussed in \cite{dh,wwf}.
More precisely, we make explicit through several examples the connection
between interpolating orbifolds and spacetime duality twists. We argue that
generic nongeometric backgrounds arising from duality twists will not have
simple orbifold constructions and then proceed to construct several examples
which do have a consistent worldsheet description.Comment: v2-references added; v3-minor correction (eqn. 4.17
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