A wide class of $1+1$ dimensional unitary conformal field theories allows for an explicit construction of nonequilibrium "profile states" interpolating smoothly between different equilibria on the left and on the right. It has been recently established that the generating function for the full counting statistics of energy transfers in such states may be expressed in terms of the solution to a non-local Riemann-Hilbert problem. Following earlier works on the statistics of energy transfers, in particular the ones of Bernard-Doyon on the "partitioning protocol" in conformal field theory, the full counting statistics of energy transfers in the profile states was conjectured to satisfy a large deviation principle in the limit of long transfer-times. The present paper establishes rigorously this conjecture by carrying out the long-time asymptotic analysis of the underlying non-local Riemann-Hilbert problem.
Employing the conformal welding technique, we find an exact expression for the Full Counting Statistics of energy transfers in a class of inhomogeneous nonequilibrium states of a (1+1)-dimensional unitary Conformal Field Theory. The expression involves the Schwarzian action of a complex field obtained by solving a Riemann-Hilbert type problem related to conformal welding of infinite cylinders. On the way, we obtain a formula for the extension of characters of unitary positive-energy representations of the Virasoro algebra to 1-parameter groups of circle diffeomorphisms and we develop technique…
We introduce a new approach to find the Tomita-Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo-Martin-Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann-Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.
According to recent arguments by the author, the conformal field theory (CFT) describing the scaling limit of the integer quantum Hall plateau transition is a deformed level-4 Wess-Zumino-Novikov-Witten model with Riemannian target space inside a complex Lie supergroup GL. After a summary of that proposal and some of its predictions, the leading irrelevant and relevant perturbations of the proposed CFT are discussed. Argued to be marginal, these result in a non-standard renormalization group (RG) flow near criticality, which calls for modified finite-size scaling analysis and may explain the l…
Virasoro Conformal Blocks and modular functor from Liouville CFT
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay（巴黎萨克雷大学，法国国家科学研究中心，奥赛数学实验室）；University of Helsinki, Department of Mathematics and Statistics（赫尔辛基大学数学与统计系）；Aix-Marseille University, Institut de Mathématiques de Marseille (I2M), and Institut Universitaire de France (IUF)（艾克斯-马赛大学，马赛数学研究所（I2M），法国大学研究院（IUF））
The CFT of SLE loop measures and the Kontsevich--Suhov conjecture
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；CNRS & CEREMADE, Université Paris-Dauphine, PSL University, France（法国国家科学研究中心与CEREMADE，巴黎第九大学，PSL大学）
