Aspects of 4d supersymmetric dynamics and geometry

Abstract

In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional supersymmetric models as compactifications of six dimensional SCFTs. We discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be naturally imbedded in the geometric constructions. The lectures mostly review results which previously appeared in the literature but also contain some unpublished derivations.

174 pages, 66 Figures; v2: references added

References in corpus (37)

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• On the Geometry of the String Landscape and the Swampland
• The Swampland: Introduction and Review
• General Gauge Mediation
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Counting Gauge Invariants: the Plethystic Program
• 6d Conformal Matter
• S-duality in N=2 supersymmetric gauge theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Four-Dimensional SCFTs from M5-Branes
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
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• Mirrors of 3d Sicilian theories
• Tinkertoys for Gaiotto Duality
• Anomaly polynomial of general 6d SCFTs
• Cardy Formulae for SUSY Theories in d=4 and d=6
• N=1 Deformations and RG Flows of N=2 SCFTs
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• Supersymmetric gauge theories with decoupled operators and chiral ring stability
• Superconformal indices for N=1 theories with multiple duals
• Anomaly polynomial of E-string theories
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• TASI 2003 Lectures on Anomalies
• (5d RG-flow) Trees in the Tropical Rain Forest
• New aspects of Argyres--Douglas theories and their dimensional reduction
• Anomalies of QFTs from M-theory and Holography
• Rank-3 antisymmetric matter on 5-brane webs
• Weakly coupled conformal manifolds in 4d
• On the compactification of 5d theories to 4d
• E_8 orbits of IR dualities
• On the 3d compactifications of 5d SCFTs associated with SU(N+1) gauge theories
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Matching higher symmetries across Intriligator-Seiberg duality
• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• Distinquishing 4d N=2 SCFTs