Flavor Symmetry of 5d SCFTs, Part 1: General Setup

TL;DR

The paper develops a geometric framework to extract the flavor symmetry of 5d SCFTs obtained from circle-compactified 6d SCFTs, by encoding non-abelian flavor symmetries in collections of non-compact ${\\mathbb P}}^1$-fibered surfaces within a CY3 and tracking their gluing to compact surfaces. It distinguishes localized and delocalized flavor symmetries on the 6d tensor-branch graph, and extends the construction to 5d KK theories with untwisted and twisted compactifications via affine algebras and folding. The method provides explicit rules for building the CY3 geometry, including the ${\\Omega}$-matrix data and gluing rules, and shows how RG flows from 5d KK theories to 5d SCFTs (via flops) produce flavor-symmetry enhancements at the conformal point. A comparative discussion with CFDs demonstrates the approach’s ability to capture flows beyond CFDs and underlines its overall robustness and applicability to a wide class of 5d SCFTs.

Abstract

A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d N=1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.