Global Anomalies and Geometric Engineering of Critical Theories in Six Dimensions

TL;DR

This paper investigates global gauge anomalies in six-dimensional theories with specific gauge groups, rules out some models with IR fixed points, and constructs new models via F-theory, linking them to heterotic string compactifications.

Contribution

It identifies global anomalies in 6D gauge theories and uses F-theory to geometrically engineer models, including new series without field theory analogs.

Findings

Global anomalies characterized by Z_{12}, Z_6, Z_3 for SU(2), SU(3), G_2.

Certain 6D N=1 QFTs with IR fixed points are ruled out due to anomalies.

Constructed infinite series of models via F-theory related to heterotic string compactifications.

Abstract

We show the existence of global gauge anomalies in six dimensions for gauge groups SU(2),SU(3) and G_2 coupled to matter, characterized by an element of Z_{12},Z_6 and Z_3 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 E_8 x E_8 heterotic string compactification on K3 with instanton numbers (12+n,12-n).