Related papers: Boundary operators in the O(n) and RSOS matrix mod…
In this paper we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator…
This article is a direct continuation of [1] where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator.…
We discuss the new integrable boundary conditions for the O(N) nonlinear $\sigma$ model and related solutions of the boundary Yang-Baxter equation, which were presented in our previous paper hep-th/0108039.
We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann…
We diagonalise the transfer matrix of boundary ABF models using bosonized vertex operators. We compute the boundary S-matrix and check the scaling limit against known results for perturbed boundary conformal field theories.
A new numerical method to determine the boundary condition changing (bcc) operators in the statistical models is introduced. This method is based on a variant of Schramm-Loewner Evolution (SLE), namely SLE(\kappa; \rho). As a prototype,…
The theory of one-sided coupled operator matrices, recently introduced by K.-J. Engel, is an abstract framework for concrete initial value problems and allows complete information on well-posedness, and stability of solutions. These notes…
We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS…
Boundary operators and boundary states in $SU(2)$-invariant Thirring model are considered from the point of view of bosonization and oscillator realizations of bulk and boundary Zamolodchikov-Faddeev algebras.
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the…
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…
We study the large $N$ limit of $O(N)$ scalar field theory with classically marginal $\phi^6$ interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large $N$. We find…
For one dimensional SU(n) Hubbard model, a pair of Lax operators are derived, which give a set of fundamental equations for the quantum inverse scattering method under both periodic and open boundary conditions. This provides another proof…
The one matrix model is known to reproduce in the continuum limit the (2,2p+1) minimal Liouville gravity. Recently, two of the authors have shown how to construct arbitrary critical boundary conditions within this matrix model. So far,…
Motivated by the Matrix Spencer conjecture, we study the problem of finding signed sums of matrices with a small matrix norm. A well-known strategy to obtain these signs is to prove, given matrices $A_1, \dots, A_n \in \mathbb{R}^{m \times…
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…
In this paper second order elliptic boundary value problems on bounded domains $\Omega\subset\dR^n$ with boundary conditions on $\partial\Omega$ depending nonlinearly on the spectral parameter are investigated in an operator theoretic…
Bounds on anomalous dimensions of scalar operators in 4d superconformal field theory are explored through perturbative viewpoint. Following the recent work of Green and Shih, in which a conjecture involved this issue is verified at the NLO,…
We investigate matrix-weighted bounds for the sublinear non-kernel operators considered by F. Bernicot, D. Frey, and S. Petermichl. We extend their result to sublinear operators acting upon vector-valued functions. First, we dominate these…
We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…