Anomalies in string theory with D-branes
type: Item
instance of: scholarly article
title: Anomalies in string theory with D-branes
zbMATH Open document ID: 1028.81052
author: Daniel S. Freed
author: Edward Witten
published in: The Asian Journal of Mathematics
publication date: 2004-01-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/9907189
review text: The authors study global anomalies in the world-sheet path integral of Type II superstring theory in the presence of D-branes. A string worldsheet consisting of an oriented surface \(\Sigma\) that is mapped to the spacetime \(Y\) with \(\partial\Sigma\) mapped to the D-brane \(Q\) is considered. There are a field \(\mathbf A\) on the \(Q\) and a Neveu-Schwarz \(\mathbf B\)-field propagating in the bulk of spacetime. In the paper the worldsheet measure is considered which contains two factors : Pfaffian of the worldsheet Dirac operator and the holonomy of a field \(A\). The main result is investigation of the anomaly in the Pfaffian : (a) the Pfaffian is not a function, but rather a section of a line bundle over the space of some parameters; (b) the anomaly is the obstruction to the existence of a global flat section of unit norm. The interpretation of the \(\mathbf A\)-field (for \(\mathbf B=0\) case) as a \(\text{Spin}^c\) connection rather than an ordinary U(1) gauge field is given. If \(\mathbf B\neq 0\) a more complicated interpretation of the \(\mathbf A\)-field is found. In this case D-brane charge takes values in a twisted form of \(K\)-theory.
reviewed by: Vladimir Dzhunushaliev
Mathematics Subject Classification ID: 81T50
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 83E30
zbMATH DE Number: 1563289
zbMATH Keywords: worldsheet measure
zbMATH Keywords: string
zbMATH Keywords: anomaly
zbMATH Keywords: D-brane
MaRDI profile type: Publication
arXiv ID: hep-th/9907189
Wikidata QID: Q125820078
OpenAlex ID: W1839514714
DOI: 10.4310/AJM.1999.V3.N4.A6
description: scientific article