1,938 research outputs found
N=1 gauge superpotentials from supergravity
We review the supergravity derivation of some non-perturbatively generated
effective superpotentials for N=1 gauge theories. Specifically, we derive the
Veneziano-Yankielowicz superpotential for pure N=1 Super Yang-Mills theory from
the warped deformed conifold solution, and the Affleck-Dine-Seiberg
superpotential for N=1 SQCD from a solution describing fractional D3-branes on
a C^3 / Z_2 x Z_2 orbifold.Comment: LaTeX, iopart class, 8 pages, 3 figures. Contribution to the
proceedings of the workshop of the RTN Network "The quantum structure of
space-time and the geometric nature of fundamental interactions", Copenhagen,
September 2003; v2: published version with minor clarification
Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry
The purpose of this paper is to provide the reader with a collection of
results which can be found in the mathematical literature and to apply them to
hyperbolic spaces that may have a role in physical theories. Specifically we
apply K-theory methods for the calculation of brane charges and RR-fields on
hyperbolic spaces (and orbifolds thereof). It is known that by tensoring
K-groups with the rationals, K-theory can be mapped to rational cohomology by
means of the Chern character isomorphisms. The Chern character allows one to
relate the analytic Dirac index with a topological index, which can be
expressed in terms of cohomological characteristic classes. We obtain explicit
formulas for Chern character, spectral invariants, and the index of a twisted
Dirac operator associated with real hyperbolic spaces. Some notes for a
bivariant version of topological K-theory (KK-theory) with its connection to
the index of the twisted Dirac operator and twisted cohomology of hyperbolic
spaces are given. Finally we concentrate on lower K-groups useful for
description of torsion charges.Comment: 26 pages, no figures, LATEX. To appear in the Classical and Quantum
Gravit
Building a Better Racetrack
We find IIb compactifications on Calabi-Yau orientifolds in which all Kahler
moduli are stabilized, along lines suggested by Kachru, Kallosh, Linde and
Trivedi.Comment: 47 pages, 1 figure, harvmac (v2: added references, minor comments,
v3: improved discussion of metastability and explicit flux vacua
Boundary fields and renormalization group flow in the two-matrix model
We analyze the Ising model on a random surface with a boundary magnetic field
using matrix model techniques. We are able to exactly calculate the disk
amplitude, boundary magnetization and bulk magnetization in the presence of a
boundary field. The results of these calculations can be interpreted in terms
of renormalization group flow induced by the boundary operator. In the
continuum limit this RG flow corresponds to the flow from non-conformal to
conformal boundary conditions which has recently been studied in flat space
theories.Comment: 31 pages, Late
The matrix factorisations of the D-model
The fundamental matrix factorisations of the D-model superpotential are found
and identified with the boundary states of the corresponding conformal field
theory. The analysis is performed for both GSO-projections. We also comment on
the relation of this analysis to the theory of surface singularities and their
orbifold description.Comment: 23 pages, LaTe
Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
We investigate orientifolds of type II string theory on K3 and Calabi-Yau
3-folds with intersecting D-branes wrapping special Lagrangian cycles. We
determine quite generically the chiral massless spectrum in terms of
topological invariants and discuss both orbifold examples and algebraic
realizations in detail. Intriguingly, the developed techniques provide an
elegant way to figure out the chiral sector of orientifold models without
computing any explicit string partition function. As a new example we derive a
non-supersymmetric Standard-like Model from an orientifold of type IIA on the
quintic Calabi-Yau 3-fold with wrapped D6-branes. In the case of supersymmetric
intersecting brane models on Calabi-Yau manifolds we discuss the D-term and
F-term potentials, the effective gauge couplings and the Green-Schwarz
mechanism. The mirror symmetric formulation of this construction is provided
within type IIB theory. We finally include a short discussion about the lift of
these models from type IIB on K3 to F-theory and from type IIA on Calabi-Yau
3-folds to M-theory on G_2 manifolds.Comment: 82 pages, harvmac, 5 figures. v2: references added. v3: T^6
orientifold corrected, JHEP versio
Introduction to Random Matrices
These notes provide an introduction to the theory of random matrices. The
central quantity studied is where is the integral
operator with kernel 1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y). Here
and is the characteristic function
of the set . In the Gaussian Unitary Ensemble (GUE) the probability that no
eigenvalues lie in is equal to . Also is a tau-function
and we present a new simplified derivation of the system of nonlinear
completely integrable equations (the 's are the independent variables)
that were first derived by Jimbo, Miwa, M{\^o}ri, and Sato in 1980. In the case
of a single interval these equations are reducible to a Painlev{\'e} V
equation. For large we give an asymptotic formula for , which is
the probability in the GUE that exactly eigenvalues lie in an interval of
length .Comment: 44 page
NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
Using the algebraic geometric approach of Berenstein et {\it al}
(hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non
commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with
discrete torsion. We first develop a new way of getting complex mirror
Calabi-Yau hypersurfaces in toric manifolds with a action and analyze the general group of the
discrete isometries of . Then we build a general class of
complex dimension NC mirror Calabi-Yau orbifolds where the non
commutativity parameters are solved in terms of discrete
torsion and toric geometry data of in which the original
Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the
NC algebra for generic dimensions NC Calabi-Yau manifolds and give various
representations depending on different choices of the Calabi-Yau toric geometry
data. We also study fractional D-branes at orbifold points. We refine and
extend the result for NC to higher dimensional torii orbifolds
in terms of Clifford algebra.Comment: 38 pages, Late
Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
We survey recent results on quantum corrections to the hypermultiplet moduli
space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or,
equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our
main focus lies on the problem of resumming the infinite series of D-brane and
NS5-brane instantons, using the mathematical machinery of automorphic forms. We
review the proposal that whenever the low-energy theory in D=3 exhibits an
arithmetic "U-duality" symmetry G(Z) the total instanton partition function
arises from a certain unitary automorphic representation of G, whose Fourier
coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1
we argue that the relevant automorphic representation falls in the quaternionic
discrete series of G, and that the partition function can be realized as a
holomorphic section on the twistor space Z over M. We also offer some comments
on the close relation with N=2 wall crossing formulae.Comment: 25 pages, contribution to the proceedings of the workshop "Algebra,
Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 201
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