M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies

TL;DR

This paper explores the relationship between M-theory compactified on elliptic Calabi-Yau threefolds and 6d anomalies, establishing a connection to F-theory and analyzing geometric properties.

Contribution

It determines charged matter content in 5d theories from geometric data and shows these theories can be lifted to 6d, linking M-theory compactifications to F-theory.

Findings

Matching intersection numbers with Chern-Simons levels

All 5d theories satisfy 6d anomaly cancellation

Computed Euler characteristics of elliptic Calabi-Yau threefolds

Abstract

We consider the 8-supercharge 5d su(N) gauge theories from M-theory compactified on elliptic Calabi-Yau threefolds. By matching the triple intersection numbers in the elliptic Calabi-Yau with the 5d Chern-Simons levels, we determine the charged matter contents for these theories. We show that all these 5d theories can be lifted to 6d N = (1, 0) theories while satisfying the anomaly cancellation equations. This suggests that the 5d theories obtained from M-theory compactified on elliptic Calabi-Yau threefolds have a natural 12d description, which as we know is F-theory. Furthermore, we compute the Euler characteristics of the elliptic Calabi-Yau threefolds.