32,295 research outputs found
Defect Perturbations in Landau-Ginzburg Models
Perturbations of B-type defects in Landau-Ginzburg models are considered. In
particular, the effect of perturbations of defects on their fusion is analyzed
in the framework of matrix factorizations. As an application, it is discussed
how fusion with perturbed defects induces perturbations on boundary conditions.
It is shown that in some classes of models all boundary perturbations can be
obtained in this way. Moreover, a universal class of perturbed defects is
constructed, whose fusion under certain conditions obey braid relations. The
functors obtained by fusing these defects with boundary conditions are twist
functors as introduced in the work of Seidel and Thomas.Comment: 46 page
The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
We present a compendium of numerical simulation techniques, based on tensor
network methods, aiming to address problems of many-body quantum mechanics on a
classical computer. The core setting of this anthology are lattice problems in
low spatial dimension at finite size, a physical scenario where tensor network
methods, both Density Matrix Renormalization Group and beyond, have long proven
to be winning strategies. Here we explore in detail the numerical frameworks
and methods employed to deal with low-dimension physical setups, from a
computational physics perspective. We focus on symmetries and closed-system
simulations in arbitrary boundary conditions, while discussing the numerical
data structures and linear algebra manipulation routines involved, which form
the core libraries of any tensor network code. At a higher level, we put the
spotlight on loop-free network geometries, discussing their advantages, and
presenting in detail algorithms to simulate low-energy equilibrium states.
Accompanied by discussions of data structures, numerical techniques and
performance, this anthology serves as a programmer's companion, as well as a
self-contained introduction and review of the basic and selected advanced
concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure
TBA for non-perturbative moduli spaces
Recently, an exact description of instanton corrections to the moduli spaces
of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau
compactifications of Type II superstring theories was found. The equations
determining the instanton contributions turn out to have the form of
Thermodynamic Bethe Ansatz. We explore further this relation and, in
particular, we identify the contact potential of quaternionic string moduli
space with the free energy of the integrable system and the Kahler potential of
the gauge theory moduli space with the Yang-Yang functional. We also show that
the corresponding S-matrix satisfies all usual constraints of 2d integrable
models, including crossing and bootstrap, and derive the associated Y-system.
Surprisingly, in the simplest case the Y-system is described by the MacMahon
function relevant for crystal melting and topological strings.Comment: 25 pages, 1 figur
Universal amplitude ratios and Coxeter geometry in the dilute A model
The leading excitations of the dilute model in regime 2 are considered
using analytic arguments. The model can be identified with the integrable
perturbation of the unitary minimal series . It is
demonstrated that the excitation spectrum of the transfer matrix satisfies the
same functional equations in terms of elliptic functions as the exact
S-matrices of the perturbation do in terms of trigonometric
functions. In particular, the bootstrap equation corresponding to a self-fusing
process is recovered. For the special cases corresponding to the
Ising model in a magnetic field, and the leading thermal perturbations of the
tricritical Ising and three-state Potts model, as well as for the unrestricted
model, , we relate the structure of the Bethe roots to the Lie
algebras and using Coxeter geometry. In these cases Coxeter
geometry also allows for a single formula in generic Lie algebraic terms
describing all four cases. For general we calculate the spectral gaps
associated with the leading excitation which allows us to compute universal
amplitude ratios characteristic of the universality class. The ratios are of
field theoretic importance as they enter the bulk vacuum expectation value of
the energy momentum tensor associated with the corresponding integrable quantum
field theories.Comment: 32 pages (tcilatex
Boundary Conditions in Rational Conformal Field Theories
We develop further the theory of Rational Conformal Field Theories (RCFTs) on
a cylinder with specified boundary conditions emphasizing the role of a triplet
of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that
solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is
equivalent to finding integer valued matrix representations of the Verlinde
algebra. These matrices allow us to naturally associate a graph to each
RCFT such that the conformal boundary conditions are labelled by the nodes of
. This approach is carried to completion for theories leading to
complete sets of conformal boundary conditions, their associated cylinder
partition functions and the -- classification. We also review the
current status for WZW theories. Finally, a systematic generalization
of the formalism of Cardy-Lewellen is developed to allow for multiplicities
arising from more general representations of the Verlinde algebra. We obtain
information on the bulk-boundary coefficients and reproduce the relevant
algebraic structures from the sewing constraints.Comment: 71 pages. Minor changes with respect to 2nd version. Recently
published in Nucl.Phys.B but mistakenly as 1st version. Will be republished
in Nucl.Phys.B as this (3rd) versio
Recommended from our members
Pseudotyping exosomes for enhanced protein delivery in mammalian cells.
Exosomes are cell-derived nanovesicles that hold promise as living vehicles for intracellular delivery of therapeutics to mammalian cells. This potential, however, is undermined by the lack of effective methods to load exosomes with therapeutic proteins and to facilitate their uptake by target cells. Here, we demonstrate how a vesicular stomatitis virus glycoprotein (VSVG) can both load protein cargo onto exosomes and increase their delivery ability via a pseudotyping mechanism. By fusing a set of fluorescent and luminescent reporters with VSVG, we show the successful targeting and incorporation of VSVG fusions into exosomes by gene transfection and fluorescence tracking. We subsequently validate our system by live cell imaging of VSVG and its participation in endosomes/exosomes that are ultimately released from transfected HEK293 cells. We show that VSVG pseudotyping of exosomes does not affect the size or distributions of the exosomes, and both the full-length VSVG and the VSVG without the ectodomain are shown to integrate into the exosomal membrane, suggesting that the ectodomain is not required for protein loading. Finally, exosomes pseudotyped with full-length VSVG are internalized by multiple-recipient cell types to a greater degree compared to exosomes loaded with VSVG without the ectodomain, confirming a role of the ectodomain in cell tropism. In summary, our work introduces a new genetically encoded pseudotyping platform to load and enhance the intracellular delivery of therapeutic proteins via exosome-based vehicles to target cells
- …