An SL(2,Z) anomaly in IIB supergravity and its F-theory interpretation
Abstract
The SL(2,Z) duality transformations of type IIB supergravity are shown to be anomalous in generic F-theory backgrounds due to the anomalous transformation of the phase of the chiral fermion determinant. The anomaly is partially cancelled provided the ten-dimensional type IIB theory lagrangian contains a term that is a ten-form made out of the composite U(1) field strength and four powers of the curvature. A residual anomaly remains uncancelled, and this implies a certain topological restriction on consistent backgrounds of the euclidean theory. A similar, but slightly stronger, restriction is also derived from an explicit F-theory compactification on K3 x M8 (where M8 is an eight-manifold with a nowhere vanishing chiral spinor) where the cancellation of tadpoles for Ramond--Ramond fields is only possible if M8 has an Euler character that is a positive multiple of 24. The interpretation of this restriction in the dual heterotic theory on T2 x M8 is also given.
Keywords
Cite
@article{arxiv.hep-th/9810153,
title = {An SL(2,Z) anomaly in IIB supergravity and its F-theory interpretation},
author = {Matthias R. Gaberdiel and Michael B. Green},
journal= {arXiv preprint arXiv:hep-th/9810153},
year = {2009}
}
Comments
Argument has been streamlined and references have been added. 18 pages, harvmac (b)