Related papers: Conformal Field Theory and Statistical Mechanics
Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent…
Conformal field theories (CFTs) in Euclidean signature satisfy well-accepted rules, such as conformal invariance and the convergent Euclidean operator product expansion (OPE). Nowadays, it is common to assume that CFT correlators exist and…
We show that the four-point functions in conformal field theory are defined as distributions on the boundary of the region of convergence of the conformal block expansion. The conformal block expansion converges in the sense of…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
This is an elementary review of our recent work on the classification of the spectra of those two-dimensional rational conformal field theories (RCFTs) whose (maximal) chiral algebras are current algebras. We classified all possible…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…
We describe applications of (perturbed) conformal field theories to two-dimensional disordered systems. We present various methods of study~: (i) {\it A direct method} in which we compute the explicit disorder dependence of the correlation…
Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity…
We propose a reformulation of quantum field theory (QFT) as a relativistic statistical field theory. This rewriting embeds a collapse model within an interacting QFT and thus provides a possible solution to the measurement problem.…
The validity of the CFT in the Tomonaga-Luttinger liquid with the $1/r^\beta$ type long-range interactions is discussed. The arguments by CFT for long-range forward scatterings predict the finite size corrections which depend on the power…
We study topological defect lines in two-dimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
A brief introduction to the subject of chiral perturbation theory ($\chi$pt) is given, including a discussion of effective field theory and application to the upcoming Bates virtual Compton scattering measurement.
We present a simple introduction to the techniques of effective field theory (EFT) and their application to QCD. For problems with more than one energy scale, the EFT approach is a useful alternative to more traditional model-building…
Talk presented at the conference on representation theory and harmonic analysis at Saclay, the talk presented the development in conformal field theory since 1968
Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…