Related papers: Random Matrices, Boundaries and Branes
Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its…
We study the two-matrix model which represents the sum over closed and open random surfaces coupled to an Ising Model. The boundary conditions are characterized by the fact that the Ising spins sitting at the vertices of the boundaries are…
In this paper we construct path integral representations of the boundary states in some special backgrounds such as the U(1) gauge field background, the linear dilaton background and the open string tachyon background. The initial purpose…
We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, enter perpendicularly into a support…
Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new…
D-branes in curved backgrounds can be treated with techniques of boundary conformal field theory. We discuss the influence of scalar condensates on such branes, i.e. perturbations of boundary conditions by marginal boundary operators. A…
The 2D off-critical q-state Potts model with boundaries was studied as a factorizable relativistic scattering theory. The scattering S-matrices for particles reflecting off the boundaries were obtained for the cases of ``fixed'' and…
General boundary conditions ("branes") for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at…
Given a D-brane background in string theory (or equivalently boundary conditions in a two-dimensional conformal field theory), classical solutions of open string field theory equations of motion are conjectured to describe new D-brane…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We work out boundary states for Type IIA string theory on a plane wave background. By directly utilizing the channel duality, the induced conditions from the open string boundary conditions are imposed on the boundary states. The resulting…
We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end…
This thesis is a study of two dimensional noncritical string theory. The main tool which is used, is the matrix model. Introductions to both the Liouville model and its matrix model formulation are included. In particular the special states…
We construct branes in the plane wave background under the inclusion of fermionic boundary fields. The resulting deformed boundary conditions in the bosonic and fermionic sectors give rise to new integrable and supersymmetric branes of type…
We study N=1 super Liouville theory on worldsheets with and without boundary. Some basic correlation functions on a sphere or a disc are obtained using the properties of degenerate representations of superconformal algebra. Boundary states…
Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend…
This course provides a self contained introduction to the general theory of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined…
The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…
In this note, we consider the six-vertex model with domain wall boundary conditions, defined on a $M\times M$ lattice, in the inhomogeneous case where the partition function depends on 2M inhomogeneities $\lambda_j$ and $\mu_k$. For a…
The central theme of this thesis is noncommutativity in string theory. We explore in detail how noncommutative structures can emerge in case of the interacting bosonic string and even in the fermionic sector of superstring theory. We have…