Related papers: Index Theorem for Domain Walls
We provide a sufficient condition for the continuous extension of isometries for the Kobayashi distance between bounded convex domains in complex Euclidean spaces having boundaries that are only slightly more regular than $\mathcal{C}^1$.…
We study the role of domain walls and their relics in the very early Universe within the framework of the mode-matching technique. Domain walls formed during the spontaneous breaking of discrete symmetries are modelled as a short lived…
A generalization of Callias' index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. The index…
An explicit canonical transformation is constructed to relate the physical subspace of Yang-Mills theory to the phase space of the ADM variables of general relativity. This maps 3+1 dimensional Yang-Mills theory to local evolution of…
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in…
The pinning phenomena of the domain wall in the presence of exchange bias is studied analytically. The analytic solution of the domain wall spin configuration is presented. Unlike the traditional solution which is symmetric, our new…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
A new state-sum formula for the evaluation of the Yang-Mills measure in the Kauffman bracket skein algebra of a closed surface is derived. The formula extends the Kauffman bracket to diagrams that lie in surfaces other than the plane. It…
We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms…
Domain walls are the transition regions between two magnetic domains. These objects have been very relevant during the last decade, not only due to their intrinsic interest in the development of novel spintronics devices but also because of…
Domain walls in N=1 supersymmetric Yang-Mills theory conjecturally support topological degrees of freedom at low energy. Domain wall junctions are thus expected to support gapless degrees of freedom. We propose a natural candidate for the…
We investigate a recent proposal to construct chiral gauge theories on the lattice using domain wall fermions. We restrict ourselves to the finite volume case, in which two domain walls are present, with modes of opposite chirality on each…
In this article we develop a worldline technique based on the method of images to study the effective action associated to Yang-Mills theories on manifolds with boundaries. We consider the possibility of having either relative or absolute…
This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…
Our results are of three types. First we describe a general procedure of adjoining polynomial variables to $A_\infty$-ring spectra whose coefficient rings satisfy certain restrictions.A host of examples of such spectra is provided by…
We define the notion of index-module for a couple of A-lattices in a vector space, A being a Dedekind ring. We apply this notion to prove by elementary means that a weak Gras conjecture (i.e for irreducible nontrivial Q-characters) holds…
In the present paper an attempt has been made to study the flat fractal Friedmann - Robertson - Walker model filled with domain walls. We have obtained the fractal equation of deceleration parameter and tension of the domain wall. It is…
We study strings between static quarks in QCD with $n_f$ adjoint fermions, including $N=1$ Super Yang-Mills (SYM), in the calculable regime on $\mathbb R^3\times \mathbb S^1$. We find that they have many qualitatively new features not…
This is a self-contained tour of the Conley index and connection matrices. The starting point is Conley's fundamental theorem of dynamical systems. There is a short stop at the necessary topological background, before we proceed to the…
We investigate hermitian Yang--Mills connections for pullback vector bundles on blow-ups of K\"ahler manifolds along submanifolds. Under some mild asumptions on the graded object of a simple and semi-stable vector bundle, we provide a…