Related papers: An Introduction to Conformal Field Theory
I explain the motivation for investigating the high energy limit of QCD and give a brief presentation of recent progress in the understanding of unitarity corrections in this kinematic regime. Special emphasis is given to the conformal…
These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…
Conformal field theories play a central role in theoretical physics with many applications ranging from condensed matter to string theory. The conformal bootstrap studies conformal field theories using mathematical consistency conditions…
This survey discusses our results and conjectures concerning supersymmetric field theories and their relationship to cohomology theories. A careful definition of supersymmetric Euclidean field theories is given, refining Segal's axioms for…
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…
We discuss the common existential theory of all or almost all completions of a global function field.
This chapter provides a pedagogical introduction to lattice quantum field theory, with strong emphasis on lattice quantum chromodynamics. The chapter reviews key foundational concepts of lattice quantum chromodynamics, as well as a broad…
A generalized theory of two-dimensional isotropic turbulence is developed based on conformal symmetry. A number of minimal models of conformal turbulence are solved under an extended constraint including both the enstrophy cascade by…
The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and…
We study examples where conformal invariance implies triviality of the underlying quantum field theory.
We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…
We investigate some aspects of the c=-2 logarithmic conformal field theory. These include the various representations related to this theory, the structures which come out of the Zhu algebra and the W algebra related to this theory. We try…
I report on work on a Lagrangian formulation for the simplest 1+1 dimensional integrable hierarchies. This formulation makes the relationship between conformal field theories and (quantized) 1+1 dimensional integrable hierarchies very…
The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs:…
In this paper I develop categorical foundations needed for a rigorous approach to the definition of conformal field theory outlined by Graeme Segal. I discuss pseudo algebras over theories and 2-theories, their pseudo morphisms, bilimits,…
We present the correspondence between Lax integrable systems with spectral parameter on a Riemann surface, and Conformal Field Theories, in quite general set-up suggested earlier by the author. This correspondence turns out to give a…
This paper is devoted to the study of conformal and projective structures, and especially their connections, in the language of 2-frames, or $G$-structures of 2nd-order. While their normal Cartan connections are well-known, we use the…