Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory

TL;DR

This paper explores electric-magnetic duality in M-theory compactifications on $G_2$ manifolds, revealing how dualities with F-theory and geometric limits produce light particles with dual charges, connecting to known superconformal theories.

Contribution

It demonstrates the realization of electric-magnetic duality in $G_2$ compactifications via F-theory duality and geometric limits, linking to Minahan-Nemeschansky theories with $E_n$ symmetry.

Findings

Duality maps D3-branes to shrinking surfaces and curves.

Light particles with electric and magnetic charges emerge in the geometric limit.

The $SL(2, Z)$ monodromy corresponds to a Fourier-Mukai transform in the dual geometry.

Abstract

We study electric-magnetic duality in compactifications of M-theory on twisted connected sum (TCS) $G_2$ manifolds via duality with F-theory. Specifically, we study the physics of the D3-branes in F-theory compactified on a Calabi-Yau fourfold $Y$, dual to a compactification of M-theory on a TCS $G_2$ manifold $X$. $\mathcal{N}=2$ supersymmetry is restored in an appropriate geometric limit. In that limit, we demonstrate that the dual of D3-branes probing seven-branes corresponds to the shrinking of certain surfaces and curves, yielding light particles that may carry both electric and magnetic charges. We provide evidence that the Minahan-Nemeschansky theories with $E_n$ flavor symmetry may be realized in this way. The $SL(2,\mathbb{Z})$ monodromy of the 3/7-brane system is dual to a Fourier-Mukai transform of the dual IIA/M-theory geometry in this limit, and we extrapolate this monodromy action to the global compactification. Away from the limit, the theory is broken to $\mathcal{N}=1$ supersymmetry by a D-term.