Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds

TL;DR

This paper explores the relationships between gauge anomalies, supersymmetry, and dualities in supergravity theories derived from Calabi-Yau threefolds, revealing constraints and connections with F-theory and M-theory compactifications.

Contribution

It provides a detailed analysis of anomaly structures, duality constraints, and phase transitions in supergravity models related to Calabi-Yau threefolds, highlighting new links with F-theory.

Findings

Duality constraints depend on specific Calabi-Yau intersection forms

Derived five-dimensional central-charge formulas

Connections established between F-theory and M-theory compactifications

Abstract

We elucidate the interplay between gauge and supersymmetry anomalies in six-dimensional $N=1$ supergravity with generalized couplings between tensor and vector multiplets. We derive the structure of the five-dimensional supergravity resulting from the $S_1$ reduction of these models and give the constraints on Chern-Simons couplings that follow from duality to $M$ theory compactified on a Calabi-Yau threefold. The duality is supported only on a restricted class of Calabi-Yau threefolds and requires a special type of intersection form. We derive five-dimensional central-charge formulas and discuss briefly the associated phase transitions. Finally, we exhibit connections with $F$-theory compactifications on Calabi-Yau manifolds that admit elliptic fibrations. This analysis suggests that $F$ theory unifies Type-$IIb$ three-branes and $M$-theory five-branes.