On the M-Theory Approach to (Compactified) 5D Field Theories

TL;DR

This paper constructs M-theory curves for 5d supersymmetric gauge theories with various gauge groups, providing a unified geometric framework that captures known bounds on matter content and extends understanding of these theories.

Contribution

It introduces a method to derive M-theory curves for 5d gauge theories with SU(N), SO(N), and Sp(2N) groups, clarifying bounds on flavor numbers and addressing special cases.

Findings

Derived M-theory curves for SU(N), SO(N), Sp(2N) theories.

Confirmed known bounds on N_f for different gauge groups.

Discussed special case of SU(2) theories.

Abstract

We construct M-theory curves associated with brane configurations of SU(N), SO(N) and $Sp(2N)$ 5d supersymmetric gauge theories compactified on a circle. From the curves we can account for all the existing different SU(N) field theories with $N_f \leq 2 N$. This is the correct bound for $N \geq 3$. We remark on the exceptional case SU(2). The bounds obtained for SO(N) and $Sp(2N)$ are $N_f\leq N-4$ and $N_f\leq 2N+4$, respectively.