3,149 research outputs found
New supersymmetric flux vacua of type II string theory and Generalized Complex Geometry
We study Minkowski supersymmetric flux vacua of type II string theory. Based
on the work by M. Grana, R. Minasian, M. Petrini and A. Tomasiello, we briefly
explain how to reformulate things in terms of Generalized Complex Geometry,
which appears to be a natural framework for these compactifications. In
particular, it provides a mathematical characterization of the internal
manifold, and one is then able to find new solutions, which cannot be
constructed as usual via T-dualities from a warped T^6 solution. Furthermore,
we discuss how, thanks to a specific change of variables, one can ease the
resolution of the orientifold projection constraints pointed out by P. Koerber
and D. Tsimpis. One is then able to find new solutions with intermediate SU(2)
structure.Comment: Contribution to the proceedings of the 4th EU RTN Workshop (09/2008,
Varna, Bulgaria), 7 page
Supersymmetric D-branes on flux backgrounds
Several aspects concerning the physics of D-branes in Type II flux
compactifications preserving minimal N=1 supersymmetry in four dimensions are
considered. It is shown how these vacua are completely characterized in terms
of properly defined generalized calibrations for D-branes and the relation with
Generalized Complex Geometry is discussed. General expressions for
superpotentials and D-terms associated with the N=1 four-dimensional
description of space-time filling D-branes are presented. The massless spectrum
of calibrated D-branes can be characterized in terms of cohomology groups of a
differential complex canonically induced on the D-branes by the underlying
generalized complex structure.Comment: 9 pages; contribution to the proceedings of the RTN project
`Constituents, Fundamental Forces and Symmetries of the Universe' conference
in Napoli, October 9 - 13, 2006; (v2) references adde
From racks to pointed Hopf algebras
A fundamental step in the classification of finite-dimensional complex
pointed Hopf algebras is the determination of all finite-dimensional Nichols
algebras of braided vector spaces arising from groups. The most important class
of braided vector spaces arising from groups is the class of braided vector
spaces (CX, c^q), where C is the field of complex numbers, X is a rack and q is
a 2-cocycle on X with values in C^*. Racks and cohomology of racks appeared
also in the work of topologists. This leads us to the study of the structure of
racks, their cohomology groups and the corresponding Nichols algebras. We will
show advances in these three directions. We classify simple racks in
group-theoretical terms; we describe projections of racks in terms of general
cocycles; we introduce a general cohomology theory of racks contaninig properly
the existing ones. We introduce a "Fourier transform" on racks of certain type;
finally, we compute some new examples of finite-dimensional Nichols algebras.Comment: 54 pages. Several minor corrections. Some references added. Same
version as will appear in Adv. Mat
Generalized geometric vacua with eight supercharges
We investigate compactifications of type II and M-theory down to with
generic fluxes that preserve eight supercharges, in the framework of
Exceptional Generalized Geometry. The geometric data and gauge fields on the
internal manifold are encoded in a pair of generalized structures corresponding
to the vector and hyper-multiplets of the reduced five-dimensional
supergravity. Supersymmetry translates into integrability conditions for these
structures, generalizing, in the case of type IIB, the Sasaki-Einstein
conditions. We show that the ten and eleven-dimensional type IIB and M-theory
Killing-spinor equations specialized to a warped background imply the
generalized integrability conditions.Comment: 38 page
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
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