# Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

## TL;DR

This paper explores the relationship between five-dimensional SCFTs and gauge theory phases through M-theory/type IIA duality, focusing on toric CY singularities and their resolutions, providing a systematic map of parameters and proposing a modified prepotential expression.

## Contribution

It offers a systematic analysis of gauge theory phases of 5d SCFTs via fiberwise M-theory/type IIA duality, especially for toric CY singularities, and proposes a new form for the Coulomb-branch prepotential.

## Key findings

- Systematic map between Kähler and Coulomb parameters.
- Different gauge phases depend on singularity resolutions.
- Modified Coulomb-branch prepotential expression.

## Abstract

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities $\mathbf{X}$ and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to $\mathbf{X}$. Focussing on the case of toric CY singularities, we analyze the "gauge-theory phases" of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type $A_{M-1}$ fibered over a real line, and the map between the K\"ahler parameters of $\mathbf{X}$ and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA "reductions" give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity $\mathbf{X}$. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d $\mathcal{N}=1$ gauge theories.