1,814 research outputs found

### BPS States, Weight Spaces and Vanishing Cycles

We review some simple group theoretical properties of BPS states, in relation
with the singular homology of level surfaces. Primary focus is on classical and
quantum N=2 supersymmetric Yang-Mills theory, though the considerations can be
applied to string theory as well.Comment: for Proceedings of ``Strings 95'', 12p, plain TeX, 6 uuencoded ps
figure

### Recent Developments in String Theory

After briefly reviewing basic concepts of perturbative string theory, we
explain in simple terms some of the new findings that created excitement among
the string physicists. These developments include non-perturbative dualities
and a unified picture that embraces the so-far known theories. (An overview for
non-experts)Comment: 16 p, latex, lprocl.sty, 12 figs, Contribution to the Proceedings of
Lepton-Photon 97. Continuous updates at
http://nxth21.cern.ch/~lerche/papers/strings.ps.g

### On the Heterotic/F-Theory Duality in Eight Dimensions

We review quantitative tests on the duality between the heterotic string on
T^2 and F-theory on K3. On the heterotic side, certain threshold corrections to
the effective action can be exactly computed at one-loop order, and the issue
is to reproduce these from geometric quantities pertaining to the K3 surface.
In doing so we learn about certain non-perturbative interactions of 7-branes.Comment: latex, 10 figs, contribution to the proceedings of Cargese 199

### Chiral Rings in Topological (W-)Gravity

Talk given at the 26th Workshop: ``From Superstrings to Supergravity", Erice
- Sicily, 5-12 December 1992. We review the superconformal properties of 2d
matter coupled to gravity, and extensions thereof. Focusing on topological
strings, we recall how the superconformal structure helps to provide a direct
link between Liouville theory coupled to matter, and matrix models. We also
construct an infinite class of new theories based on $W$-gravity.Comment: 13pages, plain te

### On the Landau-Ginzburg Realization of Topological Gravities

We study the equivariant cohomology of a class of multi-field topological LG
models, and find that such systems carry intrinsic information about
$W$-gravity. As a result, we can construct the gravitational chiral ring in
terms of LG polynomials. We find, in particular, that the spectrum of such
theories seems to be richer than so far expected. We also briefly discuss the
BRST operator for non-linear topological $W$-gravity.Comment: 26p, harvmac, 4 uuencoded PostScript figure

### Prepotential, Mirror Map and F-Theory on K3

We compute certain one-loop corrections to F^4 couplings of the heterotic
string compactified on T^2, and show that they can be characterized by
holomorphic prepotentials. We then discuss how some of these couplings can be
obtained in F-theory, or more precisely from 7-brane geometry in type IIB
language. We in particular study theories with E_8 x E_8 and SO(8)^4 gauge
symmetry, on certain one-dimensional sub-spaces of the moduli space that
correspond to constant IIB coupling. For these theories, the relevant geometry
can be mapped to Riemann surfaces. Physically, the computations amount to
non-trivial tests of the basic F-theory -- heterotic duality in eight
dimensions. Mathematically, they mean to associate holomorphic 5-point
couplings of the form (del_t)^5 G = sum[ g_l l^5 q^l/(1-q^l) ] to K3 surfaces.
This can be seen as a novel manifestation of the mirror map, acting here
between open and closed string sectors.Comment: 36 pages, 2 figures (published version

### 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

### 1/4 BPS States and Non-Perturbative Couplings in N=4 String Theories

We compute certain 2K+4-point, one-loop couplings in the type IIA string
compactified on K3 x T^2, which are related to a topological index on this
manifold. Their special feature is that they are sensitive to only short and
intermediate BPS multiplets. The couplings derive from underlying prepotentials
G[K](T,U), which can be nicely summed up into a fundamental generating
function. In the dual heterotic string on T^6, the amplitudes describe
non-perturbative gravitational corrections to K-loop amplitudes due to bound
states of fivebrane instantons with heterotic world-sheet instantons. We argue,
as a consequence, that our results also give information about instanton
configurations in six dimensional Sp(2k) gauge theories on T^6.Comment: 32 p, harvmac, 1 fig. Revision: taking the fermionic contractions
into account, the K3 elliptic genus disappear

### Exceptional SW Geometry from ALE Fibrations

We show that the genus 34 Seiberg-Witten curve underlying $N=2$ Yang-Mills
theory with gauge group $E_6$ yields physically equivalent results to the
manifold obtained by fibration of the $E_6$ ALE singularity. This reconciles a
puzzle raised by $N=2$ string duality

### 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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