2,700 research outputs found
On F-theory Quiver Models and Kac-Moody Algebras
We discuss quiver gauge models with bi-fundamental and fundamental matter
obtained from F-theory compactified on ALE spaces over a four dimensional base
space. We focus on the base geometry which consists of intersecting F0=CP1xCP1
Hirzebruch complex surfaces arranged as Dynkin graphs classified by three kinds
of Kac-Moody (KM) algebras: ordinary, i.e finite dimensional, affine and
indefinite, in particular hyperbolic. We interpret the equations defining these
three classes of generalized Lie algebras as the anomaly cancelation condition
of the corresponding N =1 F-theory quivers in four dimensions. We analyze in
some detail hyperbolic geometries obtained from the affine A base geometry by
adding a node, and we find that it can be used to incorporate fundamental
fields to a product of SU-type gauge groups and fields.Comment: 13 pages; new equations added in section 3, one reference added and
typos correcte
Superstring Theory on pp Waves with ADE Geometries
We study the BMN correspondence between certain Penrose limits of type IIB
superstrings on pp-wave orbifolds with geometries, and the set of
four-dimensional superconformal field theories constructed as
quiver gauge models classified by finite Lie algebras and affine
Kac-Moody algebras. These models have 16 preserved supercharges and
are based on systems of D3-branes and wrapped D5- and D7-branes. We derive
explicitly the metrics of these pp-wave orbifolds and show that the BMN
extension requires, in addition to D5-D5 open strings in bi-fundamental
representations, D5-D7 open strings involving orientifolds with gauge
symmetry. We also give the correspondence rule between leading string states
and gauge-invariant operators in the quiver gauge models.Comment: 62 page
Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
Motivated by studies on 4d black holes and q-deformed 2d Yang Mills theory,
and borrowing ideas from compact geometry of the blowing up of affine ADE
singularities, we build a class of local Calabi-Yau threefolds (CY^{3})
extending the local 2-torus model \mathcal{O}(m)\oplus \mathcal{O}(-m)\to
T^{2\text{}} considered in hep-th/0406058 to test OSV conjecture. We first
study toric realizations of T^{2} and then build a toric representation of
X_{3} using intersections of local Calabi-Yau threefolds \mathcal{O}(m)\oplus
\mathcal{O}(-m-2)\to \mathbb{P}^{1}. We develop the 2d \mathcal{N}=2 linear
\sigma-model for this class of toric CY^{3}s. Then we use these local
backgrounds to study partition function of 4d black holes in type IIA string
theory and the underlying q-deformed 2d quiver gauge theories. We also make
comments on 4d black holes obtained from D-branes wrapping cycles in
\mathcal{O}(\mathbf{m}) \oplus \mathcal{O}(\mathbf{-m-2}%) \to \mathcal{B}_{k}
with \mathbf{m=}(m_{1},...,m_{k}) a k-dim integer vector and \mathcal{B}_{k} a
compact complex one dimension base consisting of the intersection of k
2-spheres S_{i}^{2} with generic intersection matrix I_{ij}. We give as well
the explicit expression of the q-deformed path integral measure of the
partition function of the 2d quiver gauge theory in terms of I_{ij}.Comment: 36 pages, latex, 9 figures. References adde
Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case
Using Katz, Klemm and Vafa geometric engineering method of
supersymmetric QFTs and results on the classification of generalized
Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of
CFTs based on \textit{indefinite} singularities. We show
that the vanishing condition for the general expression of holomorphic beta
function of quiver gauge QFTs coincides exactly with the
fundamental classification theorem of KM algebras. Explicit solutions are
derived for mirror geometries of CY threefolds with \textit{% hyperbolic}
singularities.Comment: 23 pages, 4 figures, minor change
Polynomial Roots and Calabi-Yau Geometries
The examination of roots of constrained polynomials dates back at least to
Waring and to Littlewood. However, such delicate structures as fractals and
holes have only recently been found. We study the space of roots to certain
integer polynomials arising naturally in the context of Calabi-Yau spaces,
notably Poincare and Newton polynomials, and observe various salient features
and geometrical patterns.Comment: 22 pages, 13 Figure
Classification of N=2 supersymmetric CFT_{4}s: Indefinite Series
Using geometric engineering method of 4D quiver gauge
theories and results on the classification of Kac-Moody (KM) algebras, we show
on explicit examples that there exist three sectors of infrared
CFTs. Since the geometric engineering of these CFTs involve type II
strings on K3 fibered CY3 singularities, we conjecture the existence of three
kinds of singular complex surfaces containing, in addition to the two standard
classes, a third indefinite set. To illustrate this hypothesis, we give
explicit examples of K3 surfaces with H and E hyperbolic
singularities. We also derive a hierarchy of indefinite complex algebraic
geometries based on affine and T algebras going beyond the
hyperbolic subset. Such hierarchical surfaces have a remarkable signature that
is manifested by the presence of poles.Comment: 12 pages, 2 figure
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