# 6D SCFTs and Phases of 5D Theories

## TL;DR

This paper explores how 6D superconformal field theories, when reduced on a circle, lead to various 5D theories and fixed points, revealing a rich phase structure connected by geometric transitions in Calabi-Yau threefolds.

## Contribution

It establishes a unified geometric framework for understanding the phase structure and fixed points of 5D theories derived from 6D SCFTs via F-theory and M-theory.

## Key findings

- Reduction of 6D SCFTs yields 1-4 5D SCFTs
- Most reductions produce 5D quiver gauge theories
- Different phases connected by flop transitions in Calabi-Yau

## Abstract

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspondence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi--Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kahler cone of the Calabi--Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity.