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In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…

On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known…

We propose a classification of the reflection $K$-matrices (solutions of the boundary Yang-Baxter equation) for the $U_{q}[\mathrm{osp}^{\left(2\right)}\left(2|2m\right)]=U_{q}[C^{\left(2\right)}\left(m+1\right)]$ vertex-model. We have…

We extend the recently developed Izergin-Korepin analysis on the wavefunctions of the $U_q(sl_2)$ six-vertex model to the reflecting boundary conditions. Based on the Izergin-Korepin analysis, we determine the exact forms of the symmetric…

In this work we demonstrate that the Yang-Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six vertex model with domain wall boundary conditions. The homogeneous limit is studied…

We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the graded version of the $A_{n-1}^{(1)}$ affine Lie algebra, the $U_{q}[sl(m|n)^{(1)}]$ vertex model, also known as…

In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an…

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.

In this paper we give a concrete recipe how to construct triples of algebra-valued meromorphic functions on a complex vector space $\mathfrak{a}$ satisfying three coupled classical dynamical Yang-Baxter equations and an associated classical…

We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…

In this first paper, we start the analysis of correlation functions of quantum spin chains with general integrable boundary conditions. We initiate these computations for the open XXX spin 1/2 quantum chains with some unparallel magnetic…

Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…

We consider integrable models solved by the nested algebraic Bethe ansatz and associated with $\mathfrak{gl}(2|1)$ or $\mathfrak{gl}(3)$ algebra symmetry. The analogue of sum formulae, previously formulated for scalar products, is…

We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…

We present a free boson realization of the vertex operators and their duals for the solvable SOS lattice model of $A^{(1)}_{n-1}$ type. We discuss a possible connection to the calculation of the correlation functions.

We revisit the properties of total time-derivative terms as well as terms proportional to the free equation of motion (EOM) in a Schwinger-Keldysh formalism. They are relevant to the correct calculation of correlation functions of curvature…

We construct integrable boundary conditions for sl(2) coset models with central charges c=3/2-12/(m(m+2)) and m=3,4,... The associated cylinder partition functions are generating functions for the branching functions but these boundary…

We formulate $\lambda$-deformed $\sigma$-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter $\lambda$ and for…

The duality of dual resonance models is shown to imply that the four point string correlation function solves the Yang-Baxter equation. A reduction of transfer matrices to $A_l$ symmetry is described by a restriction of the KP $\tau$…

We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete…