Global Anomalies and Geometric Engineering of Critical Theories in Six Dimensions
Michael Bershadsky, Cumrun Vafa
Abstract
We show the existence of global gauge anomalies in six dimensions for gauge groups SU(2),SU(3) and G2 coupled to matter, characterized by an element of Z12,Z6 and Z3 respectively. Consideration of this anomaly rules out some of the recently proposed 6 dimensional N=1 QFT's which were conjectured to possess IR fixed point at infinite coupling. We geometrically engineer essentially all the other models with one tensor multiplet using F-theory. In addition we construct 3 infinite series using F-theory geometry which do not have field theory analogs. All these models in the maximally Higgsed phase correspond to the strong coupling behaviour of E8 x E8 heterotic string compactification on K3 with instanton numbers (12+n,12-n).
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