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Magnetic quivers for rank 2 theories

Antoine Bourget, Julius F. Grimminger, Mario Martone, Gabi Zafrir

TL;DR

This work extends the magnetic quiver program to rank-2 ${\mathcal N}=2$ SCFTs, showing that most HB geometries can be captured by unitary MQs while a subset requires orthosymplectic quivers. By leveraging 5d brane webs, Class S constructions, instanton moduli spaces, and RG-flow insights, the authors produce MQs for a large portion of the known rank-2 theories and use quiver subtraction to derive Hasse diagrams that align with independent HB analyses. The results validate the MQ approach for many theories and provide cross-checks with HB Hilbert series in N=3 and N=4 cases, while also highlighting limitations and directions for describing the remaining theories. Overall, the paper demonstrates the geometric and combinatorial power of magnetic quivers in encoding Higgs branch structure of complex 4d SCFTs and underscores the need for broader MQ frameworks at higher rank.

Abstract

In this note we construct magnetic quivers for the known rank-2 four dimensional $\mathcal{N}=2$ superconformal field theories. For every rank-1 theory one can find a unitary magnetic quiver; we observe that this is no longer possible at rank 2. Our list of magnetic quivers necessarily includes orthosymplectic quivers, in addition to unitary ones, of both the simply and non-simply laced variety. Using quiver subtraction, one can compute Higgs branch Hasse diagrams and compare with the results obtained via other methods finding nearly perfect agreement.

Magnetic quivers for rank 2 theories

TL;DR

This work extends the magnetic quiver program to rank-2 SCFTs, showing that most HB geometries can be captured by unitary MQs while a subset requires orthosymplectic quivers. By leveraging 5d brane webs, Class S constructions, instanton moduli spaces, and RG-flow insights, the authors produce MQs for a large portion of the known rank-2 theories and use quiver subtraction to derive Hasse diagrams that align with independent HB analyses. The results validate the MQ approach for many theories and provide cross-checks with HB Hilbert series in N=3 and N=4 cases, while also highlighting limitations and directions for describing the remaining theories. Overall, the paper demonstrates the geometric and combinatorial power of magnetic quivers in encoding Higgs branch structure of complex 4d SCFTs and underscores the need for broader MQ frameworks at higher rank.

Abstract

In this note we construct magnetic quivers for the known rank-2 four dimensional superconformal field theories. For every rank-1 theory one can find a unitary magnetic quiver; we observe that this is no longer possible at rank 2. Our list of magnetic quivers necessarily includes orthosymplectic quivers, in addition to unitary ones, of both the simply and non-simply laced variety. Using quiver subtraction, one can compute Higgs branch Hasse diagrams and compare with the results obtained via other methods finding nearly perfect agreement.

Paper Structure

This paper contains 6 sections, 9 equations, 2 figures.

Table of Contents

  1. Introduction and Summary
  2. Magnetic quivers of rank-2
  3. RG flows
  4. Orthosymplectic quivers
  5. A comment on N>=3 theories
  6. Hasse diagrams

Figures (2)

  • Figure 1: Patterns that appear in some magnetic quivers of 4d $\mathcal{N}=2$ SCFTs, organized in columns labeled by the folding degree $k$. In all cases, the gray dot represents the rest of the quiver. When labeled (white cells), the white dots form the corresponding (twisted) affine Dynkin diagram. The first column corresponds to the simply laced algebras in the Deligne-Cvitanović sequence. In the gray cells, the Dynkin diagrams are not folded, but the whole diagram becomes long compared to the rest of the quiver.
  • Figure 2: