Related papers: Lecture notes on conformal field theory
These are lecture notes for the course "Poisson geometry and deformation quantization" given by the author during the fall semester 2020 at the University of Zurich. The first chapter is an introduction to differential geometry, where we…
Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
These notes represent the transcript of three, 90 minute lectures given by the second author at the CRM in Barcelona in 2021 as part of the "Higher Structures and Operadic Calculus" workshop. The goal of the series was to introduce and…
In this article I describe the recently-conjectured field-string duality which suggests a class of nonsupersymmetric gauge theories which are conformal (CGT) to leading order of 1/N and some of which may be conformal for finite N. If the…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
In the lecture notes, the author will survey the development of conformal geometry on four dimensional manifolds. The topic she chooses is one on which she has been involved in the past twenty or more years: the study of the integral…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
We demonstrate in detail how the space of two-dimensional quantum field theories can be parametrized by off-shell closed string states. The dynamic equation corresponding to the condition of conformal invariance includes an infinite number…
In these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…
These notes were presented at the Young Researchers School (YRS) in Maynooth in April 2024 and provide an introduction to Conformal Field Theory CFT, Boundary Conformal Field Theory (BCFT) and Defect Conformal Field Theory (DCFT). This…
In this paper we study one-dimensional conformal field theory at finite temperature dual to the two-dimensional anti-de Sitter spacetime in the Rindler coordinates. We show that conformal symmetry for thermal two-point functions manifests…
We consider a 2-dimensional conformal field theory (CFT) obtained from twisted compactification of the 4-dimensional N=4 super Yang-Mills theory on a Riemann surface with boundary. We find the boundary conditions to preserve some of the…
These lectures give an introduction to a probabilistic approach to Liouville Quantum Field Theory developed in a joint work with F. David, R. Rhodes and V. Vargas.
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge…
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
We review known results on the relations between conformal field theory, the quantization of moduli spaces of flat PSL(2,R)-connections on Riemann surfaces, and the quantum Teichmueller theory.