531 research outputs found

### On the Heterotic World-sheet Instanton Superpotential and its individual Contributions

For supersymmetric heterotic string compactifications on a Calabi-Yau
threefold $X$ endowed with a vector bundle $V$ the world-sheet superpotential
$W$ is a sum of contributions from isolated rational curves \C in $X$; the
individual contribution is given by an exponential in the K\"ahler class of the
curve times a prefactor given essentially by the Pfaffian which depends on the
moduli of $V$ and the complex structure moduli of $X$. Solutions of $DW=0$ (or
even of $DW=W=0$) can arise either by nontrivial cancellations between the
individual terms in the summation over all contributing curves or because each
of these terms is zero already individually. Concerning the latter case
conditions on the moduli making a single Pfaffian vanish (for special moduli
values) have been investigated. However, even if corresponding moduli -
fulfilling these constraints - for the individual contribution of one curve are
known it is not at all clear whether {\em one} choice of moduli exists which
fulfills the corresponding constraints {\em for all contributing curves
simultaneously}. Clearly this will in general happen only if the conditions on
the 'individual zeroes' had already a conceptual origin which allows them to
fit together consistently. We show that this happens for a class of cases. In
the special case of spectral cover bundles we show that a relevant solution set
has an interesting location in moduli space and is related to transitions which
change the generation number.Comment: 47 page

### Three-Branes and Five-Branes in N=1 Dual String Pairs

In this note we show that in dual N=1 string vacua provided by the heterotic
string on an elliptic Calabi-Yau together with a vector bundle respectively
F-theory on Calabi-Yau fourfold the number of heterotic fivebranes necessary
for anomaly cancellation matches the number of F-theory threebranes necessary
for tadpole cancellation. This extends to the general case the work of
Friedman, Morgan and Witten, who treated the case of embedding a heterotic
$E_8\times E_8$ bundle, leaving no unbroken gauge group, where one has a smooth
Weierstrass model on the F-theory side.Comment: 22 pages, latex, minor chang

### The Neveu-Schwarz Five-Brane and its Dual Geometries

In this paper we discuss two aspects of duality transformations on the
Neveu-Schwarz (NS) 5-brane solutions in type II and heterotic string theories.
First we demonstrate that the non-extremal NS 5-brane background is U-dual to
its CGHS limit, a two-dimensional black hole times $S^3\times T^5$; an
intermediate step is provided by the near horizon geometry which is given by
the three-dimensional $BTZ_3$ black hole (being closely related to $AdS_3$)
times $S^3\times T^4$. In the second part of the paper we discuss the T-duality
between $k$ NS 5-branes and the Taub-NUT spaces respectively ALE spaces, which
are related to the resolution of the $A_{k-1}$ singularities of the non-compact
orbifold ${\bf C}^2/{\bf Z}_{k}$. In particular in the framework of N=1
supersymmetric gauge theories related to brane box constructions we give the
metric dual to two sets of intersecting NS 5-branes. In this way we get a
picture of a dual orbifold background ${\bf C}^3/ \Gamma$ which is fibered
together out of two N=2 models ($\Gamma={\bf Z}_k\times {\bf Z}_{k'}$). Finally
we also discuss the intersection of NS 5-branes with D branes, which can serve
as probes of the dual background spaces.Comment: 18pp, added reference

### BPS Action and Superpotential for Heterotic String Compactifications with Fluxes

We consider N =1 compactifications to four dimensions of heterotic string
theory in the presence of fluxes. We show that up to order O(\alpha'^2) the
associated action can be written as a sum of squares of BPS-like quantities. In
this way we prove that the equations of motion are solved by backgrounds which
fulfill the supersymmetry conditions and the Bianchi identities. We also argue
for the expression of the related superpotential and discuss the radial modulus
stabilization for a class of examples.Comment: LaTeX, 28 pages. Minor changes, one more reference added. Final
version to appear on JHE

### Heterotic String Theory on non-Kaehler Manifolds with H-Flux and Gaugino Condensate

We discuss compactifications of heterotic string theory to four dimensions in
the presence of H-fluxes, which deform the geometry of the internal manifold,
and a gaugino condensate which breaks supersymmetry. We focus on the
compensation of the two effects in order to obtain vacua with zero cosmological
constant and we comment on the effective superpotential describing these vacua.Comment: 6 page

### Perspectives on Pfaffians of Heterotic World-sheet Instantons

To fix the bundle moduli of a heterotic compactification one has to
understand the Pfaffian one-loop prefactor of the classical instanton
contribution. For compactifications on elliptically fibered Calabi-Yau spaces X
this can be made explicit for spectral bundles and world-sheet instantons
supported on rational base curves b: one can express the Pfaffian in a closed
algebraic form as a polynomial, or it may be understood as a theta-function
expression. We elucidate the connection between these two points of view via
the respective perception of the relevant spectral curve, related to its
extrinsic geometry in the ambient space (the elliptic surface in X over b) or
to its intrinsic geometry as abstract Riemann surface. We identify, within a
conceptual description, general vanishing loci of the Pfaffian, and derive
bounds on the vanishing order, relevant to solutions of W=dW=0.Comment: 40 pages; minor changes, discussion section 1.1 adde

### Superpotentials for M-theory on a G_2 holonomy manifold and Triality symmetry

For $M$-theory on the $G_2$ holonomy manifold given by the cone on {\bf
S^3}\x {\bf S^3} we consider the superpotential generated by membrane
instantons and study its transformations properties, especially under monodromy
transformations and triality symmetry. We find that the latter symmetry is,
essentially, even a symmetry of the superpotential. As in Seiberg/Witten
theory, where a flat bundle given by the periods of an universal elliptic curve
over the $u$-plane occurs, here a flat bundle related to the Heisenberg group
appears and the relevant universal object over the moduli space is related to
hyperbolic geometry.Comment: 58 pages, latex; references adde

### Non-Kaehler String Backgrounds and their Five Torsion Classes

We discuss the mathematical properties of six--dimensional non--K\"ahler
manifolds which occur in the context of ${\cal N}=1$ supersymmetric heterotic
and type IIA string compactifications with non--vanishing background H--field.
The intrinsic torsion of the associated SU(3) structures falls into five
different classes. For heterotic compactifications we present an explicit
dictionary between the supersymmetry conditions and these five torsion classes.
We show that the non--Ricci flat Iwasawa manifold solves the supersymmetry
conditions with non--zero H--field, so that it is a consistent heterotic
supersymmetric groundstate.Comment: 33 pages, LaTeX; references added; one more reference adde

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