Related papers: Index Theorem for Domain Walls
We discuss relation between lattice phenomenology of confining fields in the vacuum state of Yang-Mills theories (mostly SU(2) case) and continuum theories. In the continuum, understanding of the confinement is most straightforward in the…
We give a simple and more elementary proof that the notions of Domain of Holomorphy and Weak Domain of Holomorphy are equivalent. This proof is based on a combination of Baire's Category Theorem and Montel's Theorem. We also obtain…
We address a simple model allowing the existence of domain walls with orientational moduli localized on them. Within this model, we discuss an analytic solution and explore it in the context of previously known results. We discuss the…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
Using an annular version of the F. and M. Riesz theorem, we prove a generalization of the Rudin-Carleson theorem for finitely connected bounded domains. That is, for a continuous function on a closed set in the boundary of measure zero…
We formulate notions of subadditivity and additivity of the Yang-Mills action functional in noncommutative geometry. We identify a suitable hypothesis on spectral triples which proves that the Yang-Mills functional is always subadditive, as…
The partition function of Euclidean Yang-Mills theory on two dimensional surfaces is given by the Migdal formula. It involves the area and topological characteristics of the surface. We consider this theory on a class of infinite genus…
We review our recent work on the glueball spectrum of pure Yang-Mills theory in 2+1 dimensions. The calculations make use of Karabali-Nair corner variables in the Hamiltonian formalism, and involve a determination of the leading form of the…
A domain wall and spin supercurrent can coexist in magnets with easy-cone anisotropy owing to simultaneous spontaneous breaking of Z$_2$ and U(1) symmetries. Their interaction is theoretically investigated in quasi one-dimensional…
It is known that domain wall fermions may be used in MC simulations of vector theories. The practicality and usefulness of such an implementation is investigated in the context of the vector Schwinger model, on a 2+1 dimensional lattice.…
In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…
We give a comparison of the spectrum of Yang-Mills theory in $D=3+1$, recently derived with a strong coupling expansion, with lattice data. We verify excellent agreement also for 2$^{++}$ glueball. A deep analogy with the $D=2+1$ case is…
We present a mathematical framework for generating thick domain wall solutions to the coupled Einstein-scalar field equations which are (locally) plane symmetric. This approach leads naturally to two broad classes of wall-like solutions.…
We explicitly describe the divisor class groups and semidualizing modules for ladder determinantal rings with coefficients in an arbitrary normal domain for arbitrary ladders, not necessarily connected, and all sizes of minors.
The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…
The first and shorter part of this thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible…
Suppose M is a compact manifold with boundary. Let N be a normal covering of M. Suppose (A,T) is an elliptic differential boundary value problem on M with lift (\tilde A,\tilde T) to N. Then the von Neumann dimension of kernel and cokernel…
In this paper we are interested in understanding the structure of domains of first and second kind, a concept motivated by problems in statistical mechanics. We prove some openness property for domains of first kind with respect to a…
In pure N=1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate the N vacua have been argued, on the basis of string theory realizations, to be D-branes for the confining string. In a certain limit, this means…
In this paper we will establish a structure theorem concerning the extension of analytic objects associated to germs of dimension one foliations on surfaces, through one-dimensional barriers. As an application, an extension theorem for…