Two-dimensional models with \((0,2)\) supersymmetry: perturbative aspects
type: Item
instance of: scholarly article
title: Two-dimensional models with \((0,2)\) supersymmetry: perturbative aspects
zbMATH Open document ID: 1200.17014
published in: Advances in Theoretical and Mathematical Physics
publication date: 2008-01-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0504078
full work available at URL: https://projecteuclid.org/euclid.atmp/1183728967
review text: In this impressive paper, the author presents a very interesting and important connection between quantum sigma models with \((0,2)\)-supersymmetry from the perspective of the theory of sheafs of chiral differential operators. Although the latter theory is known in the mathematical literature [\textit{V. Gorbounov, F. Malikov, V. Schechtman}, ``Gerbes of chiral differential operators.'' Math. Res. Lett. 7, No. 1, 55--66 (2000; Zbl 0982.17013)], the approach developed is less known in the physics literature. This ansatz, in perturbation theory, among many interesting facts, leads to a new perspective of quantum field theories. The perturbation theory of such quantum field theories also admits an ech-type description, which further allows various technical simplifications. For these free field theories, analyzed from this `point of view, fermions can be neglected and bosons be described by means of a special free field theory. Obstructions to neutrality and existence conditions of Virasoro fields as anomaly cancellation are described in detail. Various examples are developed to clarify this technique. This extraordinary work constitutes a novel approach to sigma models (with the constraint of perturbation theory), and certainly opens new possibilities for their physical understanding with heavy mathematical machinery.
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 17B81
zbMATH DE Number: 5230484
zbMATH Keywords: quantum sigma models with \((0,2)\)-supersymmetry
zbMATH Keywords: sheafs of chiral differential operators
reviewed by: Rutwig Campoamor Stursberg
MaRDI profile type: Publication
arXiv ID: hep-th/0504078
OpenAlex ID: W1971746838
DOI: 10.4310/ATMP.2007.V11.N1.A1
Recommended article: Chiral algebras of (0, 2) models
Recommended article: Q4507522
Recommended article: Chiral strings, topological branes, and a generalised Weyl-invariance
Recommended article: Quantization of the nonlinear sigma model revisited
Recommended article: Canonical formalism for the σ model with torsion and N supersymmetries
Recommended article: Q3364636
Recommended article: 2D sigma models and differential Poisson algebras
Recommended article: Peculiarities of beta functions in sigma models
Recommended article: Anomalies in two-dimensional supersymmetric nonlinear sigma models
Recommended article: Two-dimensional twisted sigma models and the theory of chiral differential operators
author: Edward Witten
description: scientific article