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We review the status of integrable models from the point of view of their dynamics and integrability conditions. Some integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the…
We discuss the relation among some disk amplitudes with non-trivial boundary conditions in two-dimensional quantum gravity. They are obtained by the two-matrix model as well as the three-matirx model for the case of the tricritical Ising…
We show that the most general two--matrix model with bilinear coupling underlies $c=1$ string theory. More precisely we prove that $W_{1+\infty}$ constraints, a subset of the correlation functions and the integrable hierarchy characterizing…
We study the mass and different RR charge distributions of the BPS (p,p-2)-brane bound states in the closed string brane-like $\sigma$-model. We show that such brane bound states can be realized by introducing a constant B field in the…
We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn (KLS)…
Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical…
The Ising model on an infinite generic tree is defined as a thermodynamic limit of finite systems. A detailed description of the corresponding distribution of infinite spin configurations is given. As an application we study the…
We show that the conformally invariant boundary conditions for the three-state Potts model are exhausted by the eight known solutions. Their structure is seen to be similar to the one in a free field theory that leads to the existence of…
We reformulate the matrix models of minimal superstrings as loop gas models on random surfaces. In the continuum limit, this leads to the identification of minimal superstrings with certain bosonic string theories, to all orders in the…
We study confining strings in massive adjoint two-dimensional chromodynamics. Off-shell, as a consequence of zigzag formation, the resulting worldsheet theory provides a non-trivial dynamical realization of infinite quon statistics. Taking…
The logarithmic triplet model W_2,3 at c=0 is studied. In particular, we determine the fusion rules of the irreducible representations from first principles, and show that there exists a finite set of representations, including all…
We derive Schwinger-Dyson equations for the Wilson loops of a type IIB matrix model. Superstring coordinates are introduced through the construction of the loop space. We show that the continuum limit of the loop equation reproduces the…
The entanglement entropies of $XY$ chains and quantum Ising chains (QICs) with fixed boundary conditions are studied here. Three kinds of boundary conditions (BCs) are considered: fixed up--up or down--down (the spins at both ends are…
We discuss the open string ending on D $p$-branes in IKKT framework. First we determine the boundary conditions of Green-Schwarz superstring which are consistent with supersymmetry and $\kappa$-symmetry. We point out some subtleties arising…
A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically…
The influence of world-sheet boundary condensates on the toroidal compactification of bosonic string theories is considered. At the special points in the moduli space at which the closed-string theory possesses an enhanced unbroken $G\times…
The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light-cone gauge as a second-quantized string theory in terms of a ``matrix string'' model. The theory is defined by the neighbourhood of…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection…
We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for…