Related papers: An Introduction To The Web-Based Formalism
The paper is devoted to an algebraic analogue of a geometric approach to the classical notion of complex dilatation suggested in the paper arXiv:1701.06259 [math.CV] by the author. At the same time it provides an invariant version of this…
We describe a web of well-known dualities connecting quantum field theories in $d=1+1$ dimensions. The web is constructed by gauging ${\bf Z}_2$ global symmetries and includes a number of perennial favourites such as the Jordan-Wigner…
I summarize and discuss some recent results on formulating actions of six-dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review…
This is the written version of a series of lectures reviewing the basics of duality as applied to p-forms and sigma-models. The ideas are introduced by way of worked examples, often quite detailed. Our approach is very pedestrian and the…
We present a simple physical representation for states of the two-dimensional string theory. In order to incorporate a fundamental cutoff of the order 1/g we use a picture consisting of q-oscillators at the first-quantized level. In this…
This is the first article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. It describes how large families of field theories with N=2 supersymmetry can be described by means of Lagrangian…
This two-page note gives a non-computational derivation of the dual Steenrod algebra as the automorphisms of the formal additive group. Instead of relying on computational tools like spectral sequences and Steenrod operations, the argument…
This is the first of two papers establishing structural properties of ${\cal R}_2$.
In this talk the main features of the operator formalism for the $b-c$ systems on general algebraic curves developed in refs. [1-2] are reviewed. The first part of the talk is an introduction to the language of algebraic curves. Some…
In this paper we show how the hyperstructure concept leads to new algebraic structures and general field theories.
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
This paper is a review of the theory of abelian anyons in planar systems at an introductory level and with focus on the formalism of quantum field theory, but with the aim of clarify the connections between the mathematical structure and…
In a previous article, a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes. This formalism was…
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…
These lectures provide an introduction to the microscopic description of branes in curved backgrounds. After a brief reminder of the flat space theory, the basic principles and techniques of (rational) boundary conformal field theory are…
We make a systematic development of the non-Abelian formulation of two-form gauge fields with topological coupling with the Yang-Mills one-form connection. An analysis of the gauge structure, reducibility conditions and physical degrees of…
In this paper we propose a naive construction of 2-dimensional extended topological quantum field theories (TQFTs), which can be further generalized to the higher-dimension extended TQFTs.
The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies…
These proceedings discuss some of the highlights of recent research in Formal Theory. The topics covered range from recent progress in scattering amplitudes, quantum gravity constraints on effective field theories, AdS/CFT, flat space…
We investigate the presence of twinlike models in theories described by several real scalar fields. We focus on the first-order formalism, and we show how to build distinct scalar field theories that support the same extended solution, with…