45 research outputs found
D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}
Motivated by similarities between Fractional Quantum Hall (FQH) systems and
aspects of topological string theory on conifold, we continue in the present
paper our previous study (hep-th/0604001, hep-th/0601020) concerning FQH
droplets on conifold. Here we focus our attention on the conifold sub-varieties
\textbf{\}and\textbf{\} and study the non
commutative quantum dynamics of D1 branes wrapped on a circle. We give a matrix
model proposal for FQH droplets of point like particles on
\textbf{\}and\textbf{\} with filling fraction
. We show that the ground state of droplets on carries an isospin and gives remarkably
rise to droplets on with Cartan-Weyl charge .Comment: 25 pages, one figur
NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration
Using the algebraic geometry method of Berenstein and Leigh (BL),
hep-th/0009209 and hep-th/0105229), and considering singular toric varieties
with NC irrational torus fibration, we construct NC extensions
of complex d dimension Calabi-Yau (CY) manifolds embedded
in . We give realizations of the NC toric group, derive the constraint eqs for NC Calabi-Yau (NCCY) manifolds
embedded in and work out solutions for
their generators. We study fractional branes at singularities and show
that, due to the complete reducibility property of group
representations, there is an infinite number of non compact fractional branes
at fixed points of the NC toric group.Comment: 12 pages, LaTex, no figur
On Non Commutative Calabi-Yau Hypersurfaces
Using the algebraic geometry method of Berenstein et al (hep-th/0005087), we
reconsider the derivation of the non commutative quintic algebra
and derive new representations by choosing different
sets of Calabi-Yau charges . Next we extend these results to
higher complex dimension non commutative Calabi-Yau hypersurface algebras
. We derive and solve the set of constraint eqs
carrying the non commutative structure in terms of Calabi-Yau charges and
discrete torsion. Finally we construct the representations of
preserving manifestly the Calabi-Yau condition and give comments on the non commutative subalgebras.Comment: 16 pages, Latex. One more subsection on fractional branes, one
reference and minor changes are added. To appear in Phy. Let.
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
Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite
dimensional Hilbert space and generated by unbounded Hamiltonians. In
particular, we consider quantum harmonic and certain anharmonic lattice
systems
Monte Carlo simulation of magnetic phase transitions in Mn doped ZnO
The magnetic properties of Mn-doped ZnO semi-conductor have been investigated
using the Monte Carlo method within the Ising model. The temperature
dependences of the spontaneous magnetization, specific heat and magnetic
susceptibility have been constructed for different concentrations of magnetic
dopant Mn and different carrier concentrations. The exact values of Mn
concentration and carrier concentration at which high temperature transition
occurs are determined. An alternative for the explanation of some controversies
concerning the existence and the nature of magnetism in Mn diluted in ZnO
systems is given. Other features are also studied.Comment: 10 pages, 9 figures, To appear in Journal of Magnetism and Magnetic
Material
NC Effective Gauge Model for Multilayer FQH States
We develop an effective field model for describing FQH states with rational
filling factors that are not of Laughlin type. These kinds of systems, which
concern single layer hierarchical states and multilayer ones, were observed
experimentally; but have not yet a satisfactory non commutative effective field
description like in the case of Susskind model. Using brane analysis and
fiber bundle techniques, we first classify such states in terms of
representations characterized, amongst others, by the filling factor of the
layers; but also by proper subgroups of the underlying gauge symmetry.
Multilayer states in the lowest Landau level are interpreted in terms of
systems of branes; but hierarchical ones are realized as Fiber bundles on
which we construct explicitly. In this picture, Jain and Haldane series
are recovered as special cases and have a remarkable interpretation in terms of
Fiber bundles with specific intersection matrices. We also derive the general
NC commutative effective field and matrix models for FQH states, extending
Susskind theory, and give the general expression of the rational filling
factors as well as their non abelian gauge symmetries.Comment: 54 pages 11 figures, LaTe
From orthosymplectic structure to super topological matter
Topological supermatter is given by ordinary topological matter constrained by supersymmetry or graded supergroups such as OSP(2N|2N). Using results on super oscillators and lattice QFTd, we construct a super tight binding model on hypercubic super lattice with supercharge Q=âkFËk.qk.BËk. We first show that the algebraic triplet (Ω,G,J) of super oscillators can be derived from the OSp(2N|2N) supergroup containing the symplectic Sp(2N) and the orthogonal SO(2N) as even subgroups. Then, we apply the obtained result on super oscillating matter to super bands and investigate its topological obstructions protected by TPC symmetries. We also give a classification of the Bose/Fermi coupling matrix qk in terms of subgroups of OSp(2N|2N) and show that there are 2PN (partition of N) classes qk given by unitary subgroups of U(2)ĂU(N). Other features are also given