78 research outputs found
From ten to four and back again: how to generalize the geometry
We discuss the four-dimensional N=1 effective approach in the study of warped
type II flux compactifications with SU(3)x SU(3)-structure to AdS_4 or flat
Minkowski space-time. The non-trivial warping makes it natural to use a
supergravity formulation invariant under local complexified Weyl
transformations. We obtain the classical superpotential from a standard
argument involving domain walls and generalized calibrations and show how the
resulting F-flatness and D-flatness equations exactly reproduce the full
ten-dimensional supersymmetry equations. Furthermore, we consider the effect of
non-perturbative corrections to this superpotential arising from gaugino
condensation or Euclidean D-brane instantons. For the latter we derive the
supersymmetry conditions in N=1 flux vacua in full generality. We find that the
non-perturbative corrections induce a quantum deformation of the internal
generalized geometry. Smeared instantons allow to understand KKLT-like AdS
vacua from a ten-dimensional point of view. On the other hand, non-smeared
instantons in IIB warped Calabi-Yau compactifications 'destabilize' the
Calabi-Yau complex structure into a genuine generalized complex one. This
deformation gives a geometrical explanation of the non-trivial superpotential
for mobile D3-branes induced by the non-perturbative corrections.Comment: LaTeX, 47 pages, v2, references, hyperref added, v3, correcting small
inaccuracies in eqs. (2.6a) and (5.16
Supersymmetric sources, integrability and generalized-structure compactifications
In the context of supersymmetric compactifications of type II supergravity to
four dimensions, we show that orientifold sources can be compatible with a
generalized SU(3) x SU(3)-structure that is neither strictly SU(3) nor static
SU(2). We illustrate this with explicit examples, obtained by suitably
T-dualizing known solutions on the six-torus. In addition we prove the
following integrability statements, valid under certain mild assumptions: (a)
for general type II supergravity backgrounds with orientifold and/or D-brane
generalized-calibrated sources, the source-corrected Einstein and dilaton
equations of motion follow automatically from the supersymmetry equations once
the likewise source-corrected form equations of motion and Bianchi identities
are imposed; (b) in the special case of supersymmetric compactifications to
four-dimensional Minkowski space, the equations of motion of all fields,
including the NSNS three-form, follow automatically once the supersymmetry and
the Bianchi identities of the forms are imposed. Both (a) and (b) are equally
valid whether the sources are smeared or localized. As a byproduct we obtain
the calibration form for a space-filling NS5-brane.Comment: 32 pages, 1 table, v2: added references, v3: corrected mistake in
(4.1) leading to factor 2 mistake in (B.6), corrected (B.5), smaller typo
Reformulating Supersymmetry with a Generalized Dolbeault Operator
The conditions for N=1 supersymmetry in type II supergravity have been
previously reformulated in terms of generalized complex geometry. We improve
that reformulation so as to completely eliminate the remaining explicit
dependence on the metric. Doing so involves a natural generalization of the
Dolbeault operator. As an application, we present some general arguments about
supersymmetric moduli. In particular, a subset of them are then classified by a
certain cohomology. We also argue that the Dolbeault reformulation should make
it easier to find existence theorems for the N=1 equations.Comment: 30 pages, no figures. v2: minor correction
D-branes on AdS flux compactifications
We study D-branes in N=1 flux compactifications to AdS_4. We derive their
supersymmetry conditions and express them in terms of background generalized
calibrations. Basically because AdS has a boundary, the analysis of stability
is more subtle and qualitatively different from the usual case of Minkowski
compactifications. For instance, stable D-branes filling AdS_4 may wrap trivial
internal cycles. Our analysis gives a geometric realization of the
four-dimensional field theory approach of Freedman and collaborators.
Furthermore, the one-to-one correspondence between the supersymmetry conditions
of the background and the existence of generalized calibrations for D-branes is
clarified and extended to any supersymmetric flux background that admits a
time-like Killing vector and for which all fields are time-independent with
respect to the associated time. As explicit examples, we discuss supersymmetric
D-branes on IIA nearly Kaehler AdS_4 flux compactifications.Comment: 43 pages, 2 pictures, 1 table; v2: added references, color to figure
and corrected typo in (6.21b
Electrified branes
A geometrical form of the supersymmetry conditions for D-branes on arbitrary
type II supersymmetric backgrounds is derived, as well as the associated BPS
bounds. The treatment is general and allows to consider, for instance,
non-static configurations or D-branes supporting a non-vanishing electric flux,
hence completing previous partial results. In particular, our discussion
clarifies how the notion of calibration can be extended in order to be
applicable to the most general supersymmetric configurations. As an
exemplifying preliminary step, the procedure followed is first applied to
fundamental strings.Comment: 36 page
Generalized geometry, calibrations and supersymmetry in diverse dimensions
We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d,
preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal
supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in
two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor
equations, that there is a one-to-one correspondence between background
supersymmetry equations in pure-spinor form and D-brane generalized
calibrations; this correspondence had been known to hold in the d = 4 case.
Assuming the correspondence to hold for all d, we list the calibration forms
for all admissible D-branes, as well as the background supersymmetry equations
in pure-spinor form. We find a number of general features, including the
following: The pattern of codimensions at which each calibration form appears
exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations
implies that the internal manifold is generalized Calabi-Yau. Our results are
manifestly invariant under generalized mirror symmetry.Comment: 28 pages, 1 tabl
On moduli and effective theory of N=1 warped flux compactifications
The moduli space of N=1 type II warped compactions to flat space with generic
internal fluxes is studied. Using the underlying integrable generalized complex
structure that characterizes these vacua, the different deformations are
classified by H-twisted generalized cohomologies and identified with chiral and
linear multiplets of the effective four-dimensional theory. The Kaehler
potential for chiral fields corresponding to classically flat moduli is
discussed. As an application of the general results, type IIB warped Calabi-Yau
compactifications and other SU(3)-structure subcases are considered in more
detail.Comment: 54 pages; v3: comments and references added, version published in
JHE
On the geometry of string duals with backreacting flavors
Making use of generalized calibrated geometry and G-structures we put the
problem of finding string-duals with smeared backreacting flavor branes in a
more mathematical setting. This more formal treatment of the problem allows us
to easily smear branes without good coordinate representations, establish
constraints on the smearing form and identify a topological central charge in
the SUSY algebra. After exhibiting our methods for a series of well known
examples, we apply them to the problem of flavoring a supergravity-dual to a
d=2+1 dimensional N=2 super Yang-Mills-like theory. We find new solutions to
both the flavored and unflavored systems. Interpretating these turns out to be
difficult.Comment: 38 pages - Typos corrected and references added - As published in
JHE
D-branes in Generalized Geometry and Dirac-Born-Infeld Action
The purpose of this paper is to formulate the Dirac-Born-Infeld (DBI) action
in a framework of generalized geometry and clarify its symmetry. A D-brane is
defined as a Dirac structure where scalar fields and gauge field are treated on
an equal footing in a static gauge. We derive generalized Lie derivatives
corresponding to the diffeomorphism and B-field gauge transformations and show
that the DBI action is invariant under non-linearly realized symmetries for all
types of diffeomorphisms and B-field gauge transformations. Consequently, we
can interpret not only the scalar field but also the gauge field on the D-brane
as the generalized Nambu-Goldstone boson.Comment: 32 pages, 4 figures, ver2:typos corrected, references adde
Deformations of calibrated D-branes in flux generalized complex manifolds
We study massless deformations of generalized calibrated cycles, which
describe, in the language of generalized complex geometry, supersymmetric
D-branes in N=1 supersymmetric compactifications with fluxes. We find that the
deformations are classified by the first cohomology group of a Lie algebroid
canonically associated to the generalized calibrated cycle, seen as a
generalized complex submanifold with respect to the integrable generalized
complex structure of the bulk. We provide examples in the SU(3) structure case
and in a `genuine' generalized complex structure case. We discuss cases of
lifting of massless modes due to world-volume fluxes, background fluxes and a
generalized complex structure that changes type.Comment: 52 pages, added references, added comment on ellipticity in appendix
B, made minor changes according to instructions referee JHE
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