Related papers: The logarithmic triplet theory with boundary
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
A boundary behavior of mappings, which are closely related with Sobolev and Orlicz--Sobolev classes in the plane and in the space, is investigated. There are obtained theorems on boundary behavior of classes mentioned above.
Various structural properties of the space of symmetry breaking boundary conditions that preserve an orbifold subalgebra are established. To each such boundary condition we associate its automorphism type. It is shown that correlation…
The solution of constrained linear partial-differential equations can be described via parametric representations of linear relations. To study these representations, we provide a novel definition of boundary triplets for linear relations…
We consider the bulk $\phi^3$ deformation of the free boundary conformal field theory in the $\epsilon$ expansion. We determine the leading corrections to the scaling dimensions of boundary fundamental operators and some boundary operator…
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…
The relationship between bulk and boundary properties is one of the founding features of (Rational) Conformal Field Theory. Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice…
We find the spectrum of boundary bound states for the sine-Gordon model with Dirichlet boundary conditions, closing the bootstrap and providing a complete description of all the poles in the boundary reflection factors. The boundary…
We study the $\phi^6 - \hat{\phi}^4$ model with $O(N)$-symmetry near three dimensions. This model has a sextic bulk-interaction and a quartic boundary-interaction. The bulk two-point correlator is found upto two-loops by solving the…
The three-dimensional classical O($N$) model with a boundary has received renewed interest due to the discovery of the extraordinary-log boundary universality class for $2\leq N< N_c$. The critical value $N_c$ and the exponent of the…
We derive two sets of explicit algebraic constraint preserving boundary conditions for the linearized BSSN system. The approach can be generalized to inhomogeneous differential and evolution conditions, the examples of which are given. The…
We introduce an abstract framework for elliptic boundary value problems in a variational form. Given a non-negative quadratic form in a Hilbert space, a boundary pair consists of a bounded operator, the boundary operator, and an auxiliary…
Liouville conformal field theory is considered with conformal boundary. There is a family of conformal boundary conditions parameterized by the boundary cosmological constant, so that observables depend on the dimensional ratios of boundary…
In this note self-adjoint extensions of symmetric operators are investigated by using the abstract technique of quasi boundary triples and their Weyl functions. The main result is an extension of Theorem 2.6 in [5] which provides sufficient…
We extend the analysis of the canonical structure of the Wess-Zumino-Witten theory to the bulk and boundary coset G/H models. The phase spaces of the coset theories in the closed and in the open geometry appear to coincide with those of a…
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for…
We review the definition of bulk and boundary conformal field theory in a way suited for logarithmic conformal field theory. The notion of a maximal bulk theory which can be non-degenerately joined to a boundary theory is defined. The…
The dynamics of classical field theories is usually governed by field equations, but when fields are constrained to bounded domains it is also dependent on its boundary conditions. Usually boundary conditions are constrained by the…
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These…
In non-diagonal conformal models, the boundary fields are not directly related to the bulk spectrum. We illustrate some of their features by completing previous work of Lewellen on sewing constraints for conformal theories in the presence…