Related papers: On integrable boundaries in the 2 dimensional $O(N…
We study quantum field theories with boundary by utilizing non-invertible symmetries. We consider three kinds of boundary conditions of the four dimensional $\mathbb{Z}_2$ lattice gauge theory at the critical point as examples. The weights…
An integrable version of the supersymmetric U model with open boundary conditions and an impurity situated at one end of the chain is introduced. The model is solved through the algebraic Bethe ansatz method and the Bethe ansatz equations…
We argue that, contrary to previous claims, the supersymmetric sine-Gordon model with boundary has a two-parameter family of boundary interactions which preserves both integrability and supersymmetry. We also propose the corresponding…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and…
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…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states by closing the boundary bootstrap and gave a derivation of Al.B.…
In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate…
The sigma models on projective superspaces CP^{N+M-1|N} with topological angle theta=pi mod 2pi flow to non-unitary, logarithmic conformal field theories in the low-energy limit. In this paper, we determine the exact spectrum of these…
In this paper, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…
We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter…
An $S$-matrix is proposed for the two dimensional O(3) $\sigma$-model with a dynamical $\theta$-term (axion model). Exploiting an Abelian T-duality transformation connecting the axion model to an integrable SU(2)$\times$U(1) symmetric…
We investigate the space of massive two-dimensional theories with a global U(N) symmetry and no bound states. Following S-matrix bootstrap principles, we establish rigorous bounds on the space of consistent $2 \rightarrow 2$ scattering…
We propose a nonlinear $\sigma$-model in a curved space as a general integrable elliptic model. We construct its exact solutions and obtain energy estimates near the critical point. We consider the Pohlmeyer transformation in Euclidean…
The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed…
We study the spectrum of the scaling Lee-Yang model on a finite interval from two points of view: via a generalisation of the truncated conformal space approach to systems with boundaries, and via the boundary thermodynamic Bethe ansatz.…
This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a…
We construct local zero curvature representations for non-linear sigma models on homogeneous spaces, defined on a space-time of any dimension, following a recently proposed approach to integrable theories in dimensions higher than two. We…
This paper considers and extends spectral and scattering theory to dissipative symmetric systems that may have zero speeds and in particular to strictly dissipative boundary conditions for Maxwell's equations. Consider symmetric systems…