Related papers: Lectures on Polyfolds and Symplectic Field Theory

This paper, which is a summary (in which considerable creative license has been taken) of the author's talk at the sixth international conference on $p$-adic mathematical physics and its applications (CINVESTAV, Mexico City, October 2017),…

We summarize the parallel session B4: 'Analytic approximations, perturbation theory effective field theory methods and their applications' and the joint session B2/B4: 'Approximate solutions to Einstein equations: Methods and Applications',…

A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed…

An afinne-invariant view of generating functions of symplectic transformations of an affine symplectic space is discussed. More generally, it works for symmetric symplectic spaces. The note is completely elementary, but it yields some nice…

Semiclassical perturbation theory is investigated within the framework of axiomatic field theory. Axioms of perturbation semiclassical theory are formulated. Their correspondence with LSZ approach and Schwinger source theory is studied.…

These notes describe how perturbative on-shell and off-shell string amplitudes can be computed using string field theory. Computational methods for approximating arbitrary amplitudes are discussed, and compared with standard world-sheet…

This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…

This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the…

These talks present an overview of a tentative theory of large distance physics. For each large distance L (in dimensionless units), the theory gives two complementary descriptions of spacetime physics: quantum field theory at distances…

We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit field-derivatives that plague the high orders renormalization group treatment of shift-symmetric, derivative, theories. This technique simplifies…

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…

The increasing interest in the phenomenology of the Standard Model Effective Field Theory (SMEFT), has led to the development of a wide spectrum of public codes which implement automatically different aspects of the SMEFT for…

Elements of supergeometry are an ingredient in many contemporary classical and quantum field models involving odd fields. For instance, this is the case of SUSY field theory, BRST theory, supergravity. Addressing to theoreticians, these…

I outline the history and the original proof of the Arnold conjecture on fixed points of Hamiltonian maps for the special case of the torus, leading to a sketch of the proof for general symplectic manifolds and to Floer homology. This is…

We review recent progress in Bipartite Field Theories. We cover topics such as their gauge dynamics, emergence of toric Calabi-Yau manifolds as master and moduli spaces, string theory embedding, relationships to on-shell diagrams,…

These lecture notes provide a relatively self-contained introduction to field theoretic methods employed in the study of classical and quantum phase transitions.

The lectures provide a pedagogical introduction to the methods of CFT as applied to two-dimensional critical behaviour.

Lecture notes prepared for the 2021 SAGEX PhD School in Amplitudes hosted by the University of Copenhagen August 10th through 13th. Topics covered include: the manifestation of asymptotic symmetries via soft theorems, their organization…

These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…

In this work we study particular TQFTs in three dimensions, known as Symmetry Topological Field Theories (or SymTFTs), to identify line defects of two-dimensional CFTs arising from the compactification of 6d $(2,0)$ SCFTs on 4-manifolds…