Freed, Daniel S.; Witten, Edward Anomalies in string theory with D-branes. (English) Zbl 1028.81052 Asian J. Math. 3, No. 4, 819-851 (1999). 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. Reviewer: Vladimir Dzhunushaliev (Bishkek) Cited in 173 Documents MSC: 81T50 Anomalies in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 83E30 String and superstring theories in gravitational theory Keywords:worldsheet measure; string; anomaly; D-brane PDFBibTeX XMLCite \textit{D. S. Freed} and \textit{E. Witten}, Asian J. Math. 3, No. 4, 819--851 (1999; Zbl 1028.81052) Full Text: DOI arXiv