Generalized Green-Schwarz mechanism in F theory

TL;DR

This paper derives the anomaly polynomial for 6D gauge theories from F theory compactifications, linking matter content to geometric intersection numbers and exploring gauge theories on singular 7-branes.

Contribution

It provides a generalized anomaly cancellation mechanism in F theory, connecting geometric data to physical matter content and analyzing gauge theories on singular branes.

Findings

Derived the anomaly 8-form for 6D theories in F theory.

Connected matter content to intersection numbers on elliptic Calabi-Yau threefolds.

Discussed gauge theories on 7-branes with singularities.

Abstract

We derive the anomaly 8-form of 6-dimensional gauge theories arising in F theory compactifications on elliptic Calabi-Yau threefolds. The result allows to determine the matter content of certain such theories in terms of intersection numbers on the base of elliptic fibration. We also discuss gauge theories on 7-branes with double point singularities on the worldvolume. Applications to Type II compactifications on Hirzebruch surfaces and $P^2$ are outlined.