Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations

Abstract

We initiate a systematic study of four dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) based on the analysis of their Coulomb branch geometries. Because these SCFTs are not uniquely characterized by their scale-invariant Coulomb branch geometries we also need information on their deformations. We construct all inequivalent such deformations preserving $\mathcal{N}=2$ supersymmetry and additional physical consistency conditions in the rank 1 case. These not only include all the ones previously predicted by S-duality, but also 16 additional deformations satisfying all the known $\mathcal{N}=2$ low energy consistency conditions. All but two of these additonal deformations have recently been identified with new rank 1 SCFTs; these identifications are briefly reviewed. Some novel ingredients which are important for this study include: a discussion of RG-flows in the presence of a moduli space of vacua; a classification of local $\mathcal{N}=2$ supersymmetry-preserving deformations of unitary $\mathcal{N}=2$ SCFTs; and an analysis of charge normalizations and the Dirac quantization condition on Coulomb branches. This paper is the first in a series of three. The second paper, 1601.00011, gives the details of the explicit construction of the Coulomb branch geometries discussed here, while the third, 1609.04404, discusses the computation of central charges of the associated SCFTs.

Completely revised introduction and conclusion reflecting our current, deeper, understanding of the topic. Multiple references added

References in corpus (12)

• S-duality in N=2 supersymmetric gauge theories
• The $(2,0)$ superconformal bootstrap
• N=3 four dimensional field theories
• Tinkertoys for the Z3-twisted D4 Theory
• Comments on scaling limits of 4d N=2 theories
• Gaiotto Duality for the Twisted A_{2N-1} Series
• Chiral gauge dynamics and dynamical supersymmetry breaking
• Counting RG flows
• Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• A Family of $4D$ $\mathcal{N}=2$ Interacting SCFTs from the Twisted $A_{2N}$ Series
• Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories

Cited by in corpus (47)

• Vertex operator algebras, Higgs branches, and modular differential equations
• N=1 Deformations and RG Flows of N=2 SCFTs
• S-folds and 4d N=3 superconformal field theories
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• RG Flows and Bifurcations
• Classification of Argyres-Douglas theories from M5 branes
• Selected Topics in the Large Quantum Number Expansion
• Tackling the SDC in AdS with CFTs
• Magnetic quivers for rank 1 theories
• Universal correlation functions in rank 1 SCFTs
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Tinkertoys for the Z3-twisted D4 Theory
• Gauge theories from principally extended disconnected gauge groups
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• Special Geometry and the Swampland
• Exceptional $\mathcal{N}=3$ theories
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• 4d $\mathcal{N}=3$ indices via discrete gauging
• 4d N=2 SCFT and singularity theory Part I: Classification
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Geometry of Higgs-branch superconformal primary bundles
• Compactifications of 5d SCFTs with a twist
• Mixed OPEs in $\mathcal{N}=2$ Superconformal Theories
• Argyres-Douglas matter and N=2 dualities
• Elliptic Loci of SU(3) Vacua
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• Expanding the landscape of $\mathcal{N}$=2 rank 1 SCFTs
• Construction and classification of Coulomb branch geometries
• The Partition Function Of Argyres-Douglas Theory On A Four-Manifold
• Quantum Seiberg-Witten periods for $\mathcal{N}=2$ $SU(N_c)$ SQCD around the superconformal point
• 4d N=2 SCFT and singularity theory Part III: Rigid singularity
• On the moduli spaces of 4d $\mathcal{N}=3$ SCFTs I: triple special Kähler structure
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• Masses, Sheets and Rigid SCFTs
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• The duality covariant geometry and DSZ quantization of abelian gauge theory
• 4d $\mathcal{N}=2$ SCFTs and lisse W-algebras
• Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions
• $\mathcal{N}=3$ four dimensional field theories
• On the Chiral Ring and Vacua of $\mathcal{N}=1$ Adjoint SQCD
• On the classification of planar rank-1 d=4 N=2 superconformal field theories
• Soft supersymmetry breaking of 4d $\mathcal{N}=2$ SCFT
• Four-dimensional $\mathcal{N}=1$ SCFTs on S-folds with T-branes and AdS/CFT correspondence