The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories

Abstract

Superconformal field theory with $\mathcal{N}=2$ supersymmetry in four dimensional spacetime provides a prime playground to study strongly coupled phenomena in quantum field theory. Its rigid structure ensures valuable analytic control over non-perturbative effects, yet the theory is still flexible enough to incorporate a large landscape of quantum systems. Here we aim to offer a guidebook to fundamental features of the 4d $\mathcal{N}=2$ superconformal field theories and basic tools to construct them in string/M-/F-theory. The content is based on a series of lectures at the Quantum Field Theories and Geometry School (https://sites.google.com/view/qftandgeometrysummerschool/home) in July 2020.

v3: Improved discussion, fixed typos, added references v2: Typos fixed and added references. v1: 96 pages. Based on a series of lectures at the Quantum Field Theories and Geometry School in July 2020

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• Generalized Global Symmetries
• The Refined Topological Vertex
• S-duality in N=2 supersymmetric gauge theories
• Mirrors of 3d Sicilian theories
• Tinkertoys for Gaiotto Duality
• N=1 Deformations and RG Flows of N=2 SCFTs
• Correlation functions in conformal Toda field theory I
• A non-renormalization theorem for chiral primary 3-point functions
• A holographic computation of the central charges of d=4, N=2 SCFTs
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Lagrangians for generalized Argyres-Douglas theories
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• 2-Group Symmetries in Class S
• Higher-Form Symmetries and Their Anomalies in M-/F-Theory Duality
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• N=1 Lagrangians for generalized Argyres-Douglas theories
• Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations
• Branes and the Kraft-Procesi Transition
• (5d RG-flow) Trees in the Tropical Rain Forest
• Half-BPS supergravity solutions and superalgebras
• New aspects of Argyres--Douglas theories and their dimensional reduction
• M5-brane Sources, Holography, and Argyres-Douglas Theories
• N=2 S-duality Revisited
• Holographic Duals of Argyres-Douglas Theories
• Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)
• More Three Dimensional Mirror Pairs
• 1-Form Symmetry, Isolated N=2 SCFTs, and Calabi-Yau Threefolds
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• N=2 S-duality via Outer-automorphism Twists
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Magnetic quivers for rank 2 theories
• Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• Higgs Branches of U/SU Quivers via Brane Locking
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
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• Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories
• Resolving spacetime singularities in flux compactifications & KKLT
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Line Defects in Three Dimensional Mirror Symmetry beyond Linear Quivers
• On the compactification of 5d theories to 4d
• Discrete gauging and Hasse diagrams
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Cited by in corpus (4)

• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• A tale of 2-groups: D${}_p$(USp(2N)) theories
• Linear Quivers at Large-$N$
• Disconnected gauge groups in the infrared