1,034 research outputs found
On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds
We derive the complete supergravity description of the N=2 scalar potential
which realizes a generic flux-compactification on a Calabi-Yau manifold
(generalized geometry). The effective potential V_{eff}=V_{(\partial_Z V=0)},
obtained by integrating out the massive axionic fields of the special
quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with
respect to {\rm Sp}(2 h_2+2)\times {\rm Sp}(2 h_1+2) and their exchange, being
h_1, h_2 the complex dimensions of the underlying special geometries. {\Scr
V}_{eff} has a manifestly N=1 form in terms of a mirror symmetric
superpotential W$ proposed, some time ago, by Berglund and Mayr.Comment: 14 pages, LaTeX sourc
N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures
We consider backgrounds of (massive) IIA supergravity of the form of a warped
product , where is a six-dimensional compact
manifold and is or a four-dimensional Minkowski space. We
analyse conditions for and supersymmetry on
manifolds of SU(2) structure. We prove the absence of solutions in certain
cases.Comment: 24 pages; v2: reference adde
How does aromaticity rule the thermodynamic stability of hydroporphyrins?
Several measures of aromaticity including energetic, magnetic, and electron density criteria are employed to show how aromatic stabilization can explain the stability sequence of hydroporphyrins, ranging from porphin to octahydroporphin, and their preferred hydrogenation paths. The methods employed involve topological resonance energies and their circuit energy effects, bond resonance energies, multicenter delocalization indices, ring current maps, magnetic susceptibilities, and nuclear-independent chemical shifts. To compare the information obtained by the different methods, the results have been put in the same scale by using recently proposed approaches. It is found that all of them provide essentially the same information and lead to similar conclusions. Also, hydrogenation energies along different hydrogenation paths connecting porphin with octahydroporphin have been calculated with density functional theory. It is shown by using the methods mentioned above that the relative stability of different hydroporphyrin isomers and the observed inaccessibility of octahydroporphin both synthetically and in nature can be perfectly rationalized in terms of aromaticity
Towards reduction of type II theories on SU(3) structure manifolds
We revisit the reduction of type II supergravity on SU(3) structure
manifolds, conjectured to lead to gauged N=2 supergravity in 4 dimensions. The
reduction proceeds by expanding the invariant 2- and 3-forms of the SU(3)
structure as well as the gauge potentials of the type II theory in the same set
of forms, the analogues of harmonic forms in the case of Calabi-Yau reductions.
By focussing on the metric sector, we arrive at a list of constraints these
expansion forms should satisfy to yield a base point independent reduction.
Identifying these constraints is a first step towards a first-principles
reduction of type II on SU(3) structure manifolds.Comment: 20 pages; v2: condition (2.13old) on expansion forms weakened,
replaced by (2.13new), (2.14new
Three Dimensional Topological Field Theory induced from Generalized Complex Structure
We construct a three-dimensional topological sigma model which is induced
from a generalized complex structure on a target generalized complex manifold.
This model is constructed from maps from a three-dimensional manifold to an
arbitrary generalized complex manifold . The theory is invariant under the
diffeomorphism on the world volume and the -transformation on the
generalized complex structure. Moreover the model is manifestly invariant under
the mirror symmetry. We derive from this model the Zucchini's two dimensional
topological sigma model with a generalized complex structure as a boundary
action on . As a special case, we obtain three dimensional
realization of a WZ-Poisson manifold.Comment: 18 page
Canonical differential geometry of string backgrounds
String backgrounds and D-branes do not possess the structure of Lorentzian
manifolds, but that of manifolds with area metric. Area metric geometry is a
true generalization of metric geometry, which in particular may accommodate a
B-field. While an area metric does not determine a connection, we identify the
appropriate differential geometric structure which is of relevance for the
minimal surface equation in such a generalized geometry. In particular the
notion of a derivative action of areas on areas emerges naturally. Area metric
geometry provides new tools in differential geometry, which promise to play a
role in the description of gravitational dynamics on D-branes.Comment: 20 pages, no figures, improved journal versio
Conifolds and Geometric Transitions
Conifold geometries have recieved a lot of attention in string theory and
string-inspired cosmology recently, in particular the Klebanov-Strassler
background that is known as the "warped throat". It is our intention in this
article to give a pedagogical explanation for the singularity resolution in
this geometry and emphasise its connection to geometric transitions. The first
part focuses on the gauge theory dual to the Klebanov-Strassler background,
which we also explain from a T-dual intersecting branes scenario. We then make
the connection to the Gopakumar-Vafa conjecture for open/closed string duality
and summarise a series of papers verifying this model on the supergravity
level.
An appendix provides extensive background material about conifold geometries.
We pay special attention to their complex structures and re-evaluate the
supersymmetry conditions on the background flux in constructions with
fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando
Zayas-Tseytlin) conifolds. We agree with earlier results that only the singular
solution allows a supersymmetric flux, but point out the importance of using
the correct complex structure to reach this conclusion.Comment: 37 pages, v3: accepted for publication in Reviews of Modern Physic
Heterotic compactifications and nearly-Kahler manifolds
We propose that under certain conditions heterotic string compactifications
on half-flat and nearly-Kahler manifolds are equivalent. Based on this
correspondence we argue that the moduli space of the nearly-Kahler manifolds
under discussion consists only of the Kahler deformations moduli space and
there is no correspondent for the complex structure deformations.Comment: 5 pages, references added, typos correcte
Generalized structures of N=1 vacua
We characterize N=1 vacua of type II theories in terms of generalized complex
structure on the internal manifold M. The structure group of T(M) + T*(M) being
SU(3) x SU(3) implies the existence of two pure spinors Phi_1 and Phi_2. The
conditions for preserving N=1 supersymmetry turn out to be simple
generalizations of equations that have appeared in the context of N=2 and
topological strings. They are (d + H wedge) Phi_1=0 and (d + H wedge) Phi_2 =
F_RR. The equation for the first pure spinor implies that the internal space is
a twisted generalized Calabi-Yau manifold of a hybrid complex-symplectic type,
while the RR-fields serve as an integrability defect for the second.Comment: 21 pages. v2, v3: minor changes and correction
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