Coulomb branches with complex singularities

Abstract

We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of $\mathcal{N}=4$ superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as $\mathcal{N}=4$ sYM theories with disconnected gauge groups.

arXiv comment43 pages

References in corpus (16)

• Evidence for F-Theory
• N=2 dualities
• Reading between the lines of four-dimensional gauge theories
• Self-Dual Strings and N=2 Supersymmetric Field Theory
• Counting Gauge Invariants: the Plethystic Program
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Tinkertoys for Gaiotto Duality
• Notes on Theories with 16 Supercharges
• Exactly Marginal Deformations and Global Symmetries
• The $\mathcal{N}=2$ superconformal bootstrap
• N=3 four dimensional field theories
• 4d $\mathcal{N}$=2 theories with disconnected gauge groups
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• S-duality in N=4 supersymmetric gauge theories
• On S-duality for Non-Simply-Laced Gauge Groups
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated

Cited by in corpus (21)

• VOAs labelled by complex reflection groups and 4d SCFTs
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• New N=2 superconformal field theories from S-folds
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Fibrations and Hasse diagrams for 6d SCFTs
• Towards the classification of rank-$r$ $\mathcal{N}=2$ SCFTs. Part I: twisted partition function and central charge formulae
• 4d $\mathcal{N}=3$ indices via discrete gauging
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Discrete gauging and Hasse diagrams
• Universality of Toda equation in $\mathcal{N}=2$ superconformal field theories
• Homological Classification of 4d $\mathcal{N}=2$ QFT. Part I: Rank-1 revisited
• (Mis-)Matching Type-B Anomalies on the Higgs Branch
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Classification of all $\mathcal{N}\ge 3$ moduli space orbifold geometries at rank 2
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• BPS Partition Functions for S-folds
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories
• N = 3 SCFTs in 4 dimensions and non-simply laced groups
• Flavor symmetries and the topology of special Kähler structures at rank 1
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