228 research outputs found
A Search for Non-Perturbative Dualities of Local Yang--Mills Theories from Calabi--Yau Threefolds
The generalisation of the rigid special geometry of the vector multiplet
quantum moduli space to the case of supergravity is discussed through the
notion of a dynamical Calabi--Yau threefold. Duality symmetries of this
manifold are connected with the analogous dualities associated with the
dynamical Riemann surface of the rigid theory. N=2 rigid gauge theories are
reviewed in a framework ready for comparison with the local case. As a
byproduct we give in general the full duality group (quantum monodromy) for an
arbitrary rigid gauge theory, extending previous explicit
constructions for the cases. In the coupling to gravity, R--symmetry
and monodromy groups of the dynamical Riemann surface, whose structure we
discuss in detail, are embedded into the symplectic duality group
associated with the moduli space of the dynamical Calabi--Yau threefold.Comment: Latex. Version of previous paper with enlarged and revised appendix
35 pages, plain LaTe
Preconditioners for Krylov subspace methods: An overview
When simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large-scale systems of equations. One major class of solution methods is that of preconditioned iterative methods, involving preconditioners which are computationally cheap to apply while also capturing information contained in the linear system. In this article, we give a short survey of the field of preconditioning. We introduce a range of preconditioners for partial differential equations, followed by optimization problems, before discussing preconditioners constructed with less standard objectives in mind
Open string modes at brane intersections
We study systematically the open string modes of a general class of BPS
intersections of branes. We work in the approximation in which one of the
branes is considered as a probe embedded in the near-horizon geometry generated
by the other type of branes. We mostly concentrate on the D3-D5 and D3-D3
intersections, which are dual to defect theories with a massive hypermultiplet
confined to the defect. In these cases we are able to obtain analytical
expressions for the fluctuation modes of the probe and to compute the
corresponding mass spectra of the dual operators in closed form. Other BPS
intersections are also studied and their fluctuation modes and spectra are
found numerically.Comment: 58 pages, 3 figures, LaTeX;v2: typos correcte
Lectures on Special Kahler Geometry and Electric--Magnetic Duality Rotations
In these lectures I review the general structure of electric--magnetic
duality rotations in every even space--time dimension. In four dimensions,
which is my main concern, I discuss the general issue of symplectic covariance
and how it relates to the typical geometric structures involved by N=2
supersymmetry, namely Special K\"ahler geometry for the vector multiplets and
either HyperK\"ahler or Quaternionic geometry for the hypermultiplets. I
discuss classical continuous dualities versus non--perturbative discrete
dualities. How the moduli space geometry of an auxiliary dynamical Riemann
surface (or Calabi--Yau threefold) relates to exact space--time dualities is
exemplified in detail for the Seiberg Witten model of an gauge theory.Comment: 56 pages, LaTeX, article.sty, espcrc2.sty. Lecture notes at Trieste
Spring School 199
FQHE and tt* Geometry
Cumrun Vafa proposed a new unifying model for the principal series of FQHE
which predicts non-Abelian statistics of the quasi-holes. The many-body
Hamiltonian supporting these topological phases of matter is invariant under
four supersymmetries. In the thesis we study the geometrical properties of this
Landau-Ginzburg theory. The emerging picture is in agreement with the Vafa's
predictions. The -SQM Vafa Hamiltonian is shown to capture the topological
order of FQHE and the monodromy representation of the braid group
factors through a Temperley-Lieb/Hecke algebra with .
In particular, the quasi-holes have the same non-Abelian braiding properties of
the degenerate field in Virasoro minimal models. Part of the
thesis is dedicated to minor results about the geometrical properties of the
Vafa model for the case of a single electron. In particular, we study a special
class of models which reveal a beautiful connection between the physics of
quantum Hall effect and the geometry of modular curves. Despite it is not
relevant for phenomenological purposes, this class of theories has remarkable
properties which enlarge further the rich mathematical structure of FQHE.Comment: Doctoral thesis, SISSA, Trieste, Italy (2019
Toward Realistic Intersecting D-Brane Models
We provide a pedagogical introduction to a recently studied class of
phenomenologically interesting string models, known as Intersecting D-Brane
Models. The gauge fields of the Standard-Model are localized on D-branes
wrapping certain compact cycles on an underlying geometry, whose intersections
can give rise to chiral fermions. We address the basic issues and also provide
an overview of the recent activity in this field. This article is intended to
serve non-experts with explanations of the fundamental aspects, and also to
provide some orientation for both experts and non-experts in this active field
of string phenomenology.Comment: 85 pages, 8 figures, Latex, Bibtex, v2: refs added, typos correcte
The -map, Tits Satake subalgebras and the search for inflaton potentials
In this paper we address the general problem of including inflationary models
exhibiting Starobinsky-like potentials into (symmetric)
supergravities. This is done by gauging suitable abelian isometries of the
hypermultiplet sector and then truncating the resulting theory to a single
scalar field. By using the characteristic properties of the global symmetry
groups of the supergravities we are able to make a general
statement on the possible -attractor models which can obtained upon
truncation. We find that in symmetric models group theoretical
constraints restrict the allowed values of the parameter to be
. This confirms and generalizes results
recently obtained in the literature. Our analysis heavily relies on the
mathematical structure of symmetric supergravities, in
particular on the so called -map connection between Quaternionic K\"ahler
manifolds starting from Special K\"ahler ones. A general statement on the
possible consistent truncations of the gauged models, leading to
Starobinsky-like potentials, requires the essential help of Tits Satake
universality classes. The paper is mathematically self-contained and aims at
presenting the involved mathematical structures to a public not only of
physicists but also of mathematicians. To this end the main mathematical
structures and the general gauging procedure of supergravities
is reviewed in some detail.Comment: 101 pages, LaTeX sourc
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