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

TL;DR

This work analyzes the low-energy limit of six-dimensional N=1 supergravity with multiple tensor and vector multiplets, clarifying how gauge and supersymmetry anomalies interplay and how circle reduction to five dimensions yields a CS-dominated theory governed by Calabi–Yau intersection numbers. The authors derive five-dimensional central charges and explore phase transitions, including tensionless strings, and show how duality to M-theory on CY3 imposes strong constraints on the CY intersection form, with elliptic fibrations naturally fitting the required structure. They connect these results to F-theory compactifications, illustrating how certain χ=0 CY manifolds realize dual M-/F-/heterotic descriptions and revealing a broader symmetry between tensor and vector sectors in special cases. Finally, they propose a twelve-dimensional interpretation via a T12 coupling that encapsulates F-theory’s unifying role for M-theory and Type IIb branes, highlighting a metric-free framework for brane interactions across M- and F-theory landscapes.

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.