6,492 research outputs found

### Conformal Field Theories on K3 and Three-Dimensional Gauge Theories

According to a recent conjecture, the moduli space of the heterotic conformal
field theory on a $G\subset$ ADE singularity of an ALE space is equivalent to
the moduli space of a pure \cx N=4 supersymmetric three-dimensional gauge
theory with gauge group G. We establish this relation using geometric
engineering of heterotic strings and generalize it to theories with non-trivial
matter content. A similar equivalence is found between the moduli of heterotic
CFT on isolated Calabi--Yau 3-fold singularities and two-dimensional
Kazama-Suzuki coset theories.Comment: 11pp, harvmac, v2: a relation between heterotic CFT on Calabi-Yau
3-fold singularities and Kazama-Suzuki models has been adde

### N=1 Mirror Symmetry and Open/Closed String Duality

We show that the exact N=1 superpotential of a class of 4d string
compactifications is computed by the closed topological string compactified to
two dimensions. A relation to the open topological string is used to define a
special geometry for N=1 mirror symmetry. Flat coordinates, an N=1 mirror map
for chiral multiplets and the exact instanton corrected superpotential are
obtained from the periods of a system of differential equations. The result
points to a new class of open/closed string dualities which map individual
string world-sheets with boundary to ones without. It predicts an
mathematically unexpected coincidence of the closed string Gromov-Witten
invariants of one Calabi-Yau geometry with the open string invariants of the
dual Calabi-Yau.Comment: harvmac, 29 pages (b), 3 figures; v2: references adde

### Summing up Open String Instantons and N=1 String Amplitudes

We compute the instanton expansions of the holomorphic couplings in the
effective action of certain \cx N=1 supersymmetric four-dimensional open
string vacua. These include the superpotential $W(\phi)$, the gauge kinetic
function $f(\phi)$ and a series of other holomorphic couplings which are known
to be related to amplitudes of topological open strings at higher world-sheet
topologies. The results are in full agreement with the interpretation of the
holomorphic couplings as counting functions of BPS domain walls. Similar
techniques are used to compute genus one partition function for the closed
topological string on Calabi--Yau 4-fold which gives rise to a theory with the
same number of supercharges in two dimensions.Comment: 29 pages harvmac(b); v2: references adde

### Non-perturbative N=1 strings from geometric singularities

The study of curved D-brane geometries in type II strings implies a general
relation between local singularities \cx W of Calabi-Yau manifolds and
gravity free supersymmetric QFT's. The minimal supersymmetric case is described
by F-theory compactifications on \cx W and can be used as a starting point to
define minimal supersymmetric heterotic string compactifications on compact
Calabi-Yau manifolds with holomorphic, stable gauge backgrounds. The geometric
construction generalizes to non-perturbative vacua with five-branes and
provides a framework to study non-perturbative dynamics of the heterotic
theory.Comment: LaTex, 11 p

### Stringy World Branes and Exponential Hierarchies

We describe heterotic string and M-theory realizations of the Randall-Sundrum
(RS) scenario with \cx N=2 and \cx N=1 supersymmetry in the bulk.
Supersymmetry can be broken only on the world brane, a scenario that has been
proposed to account for the smallness of the cosmological constant. An
interesting prediction from string duality is the generation of a warp factor
for conventional type II Calabi--Yau 3-fold compactifications. On the other
hand we argue that an assumption that is needed in the RS explanation of the
hierarchy is hard to satisfy in the string theory context.Comment: 18 pages, harvmac; references adde

### Stability of vector bundles from F-theory

We use a recently proposed formulation of stable holomorphic vector bundles
$V$ on elliptically fibered Calabi--Yau n-fold $Z_n$ in terms of toric geometry
to describe stability conditions on $V$. Using the toric map $f: W_{n+1} \to
(V,Z_n)$ that identifies dual pairs of F-theory/heterotic duality we show how
stability can be related to the existence of holomorphic sections of a certain
line bundle that is part of the toric construction.Comment: 8 pages, harvmac (b

### On N=1 Mirror Symmetry for Open Type II Strings

We study the open string extension of the mirror map for N=1 supersymmetric
type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition
is given in terms of a system of differential equations that annihilate certain
period and chain integrals. The solutions describe the flat coordinates on the
N=1 parameter space, and the exact disc instanton corrected superpotential on
the D-brane world-volume. A gauged linear sigma model for the combined
open-closed string system is also given. It allows to use methods of toric
geometry to describe D-brane phase transitions and the N=1 K\"ahler cone.
Applications to a variety of D-brane geometries are described in some detail.Comment: harvmac, 35 pages (b), 2 figures; v2: typos & references correcte

### A new kind of McKay correspondence from non-Abelian gauge theories

The boundary chiral ring of a 2d gauged linear sigma model on a K\"ahler
manifold $X$ classifies the topological D-brane sectors and the massless open
strings between them. While it is determined at small volume by simple group
theory, its continuation to generic volume provides highly non-trivial
information about the $D$-branes on $X$, related to the derived category
$D^\flat(X)$. We use this correspondence to elaborate on an extended notion of
McKay correspondence that captures more general than orbifold singularities. As
an illustration, we work out this new notion of McKay correspondence for a
class of non-compact Calabi-Yau singularities related to Grassmannians.Comment: 29 pages, harvmac(b), 2 fig

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