Related papers: Quantization of Lax integrable systems and Conform…
We consider the matrix regularization of scalar fields on a Riemann surface with a general gauge-field background. We propose a construction of the fuzzy version of the Laplacian.
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
In this letter, we continue the work we started at a previous paper and we propose new series of integrable models in quantum field theory. These models are obtained as perturbed models of the minimal conformal field theories on the…
We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the…
This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…
We give a self-contained introduction to the relations between Integrable Systems and the Geometry of Riemann Surfaces. We start from a historical introduction to the topic of integrable systems. Afterwards, we study the polynomial…
From conformal field theory on the Riemann sphere, we implement its boundary version in a simply-connected domain using the Schottky double construction. We consider the statistical fields generated by background charge modification of the…
The relation between integrable systems and algebraic geometry is known since the XIXth century. The modern approach is to represent an integrable system as a Lax equation with spectral parameter. In this approach, the integrals of the…
The classical uniformization theorem states that any simply connected Riemann surface is conformally equivalent to the disk, the plane, or the sphere, each equipped with a standard conformal structure. We give a similar uniformization for…
We show how the superintegrability of certain systems can be deduced from the presence of multiple parameters in the rational Lax matrix representation. This is also related to the fact that such systems admit a separation of variables in…
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…
The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
We study the gluing theory of Riemann surfaces using formal algebraic geometry, and give computable relations between the associated parameters for different gluing processes. As its application to the Liouville conformal field theory, we…
We review some aspects of logarithmic conformal field theories which might shed some light on the geometrical meaning of logarithmic operators. We consider an approach, put forward by V. Knizhnik, where computation of correlation functions…
Conformal field theory gives quite detailed predictions for the low energy spectrum and scaling exponents of a massless Luttinger liquid at generic filling in the presence of an impurity. While these predictions were verified for…
This article provides a detailed and rigorous study of $4d$ semi-holomorphic Chern-Simons theories and their associated $2d$ integrable field theories from the homological perspective of $L_\infty$-algebras. Through the use of homotopy…
We propose an analytical approach to the conformal mapping of (rectangular) polygons based on the theory of Riemann surfaces and theta functions.