Lectures on 4d N=1 dynamics and related topics

Abstract

This lecture series consists of mostly independent three parts: Part 1: a tour of basic 4d N=1 supersymmetric dynamics, covering the pure super Yang-Mills, the Seiberg duality for classical groups, the supersymmetric index on S^3, and the a-maximization. Part 2: a brief look at 2d N=(2,2) and N=(0,2) dynamics, covering the Landau-Ginzburg and Calabi-Yau models, the elliptic genera on T^2, and the triality of Gadde-Gukov-Putrov. Appendix: a review of basic properties of supersymmetries in various dimensions. Part of the content is based on an unpublished collaboration with F. Yagi and another with K. Kikuchi.

Any type of comments will be greatly appreciated. 160 pages. Based on lectures at Tohoku University, Osaka University, Kyoto University and Nagoya University in the last several years; v2: minor typos fixed

References in corpus (75)

• Generalized Global Symmetries
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• On Renormalization Group Flows in Four Dimensions
• Coupling a QFT to a TQFT and Duality
• Reading between the lines of four-dimensional gauge theories
• Theta, Time Reversal, and Temperature
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory
• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• An Infinite Family of Superconformal Quiver Gauge Theories with Sasaki-Einstein Duals
• Elliptic genera of 2d N=2 gauge theories
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Beyond eta/s = 1/4pi
• 3d dualities from 4d dualities
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Comments on Unparticles
• Exact two-dimensional superconformal R-symmetry and c-extremization
• 3d dualities from 4d dualities for orthogonal groups
• N=1 Deformations and RG Flows of N=2 SCFTs
• A Proof of the Conformal Collider Bounds
• New checks and subtleties for AdS/CFT and a-maximization
• N=3 four dimensional field theories
• R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization
• Central Charges and $U(1{)}_R$ Symmetries in $\mathcal{N}=1$ Super Yang-Mills
• The gravity duals of N=2 superconformal field theories
• Supersymmetry enhancement by monopole operators
• Supersymmetric Index In Four-Dimensional Gauge Theories
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• A holographic computation of the central charges of d=4, N=2 SCFTs
• (0,2) Trialities
• Lagrangians for generalized Argyres-Douglas theories
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• String universality in ten dimensions
• Sasaki-Einstein Metrics on S^2 x S^3
• Superconformal indices for N=1 theories with multiple duals
• Calculating the Superconformal Index and Seiberg Duality
• Stress-tensor OPE in N=2 Superconformal Theories
• N=2 supersymmetric dynamics for pedestrians
• Line Operators in the Standard Model
• An E7 Surprise
• RG Fixed Points and Flows in SQCD with Adjoints
• Abelianization and Sequential Confinement in $2+1$ dimensions
• New Instanton Effects In Supersymmetric QCD
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• TASI 2003 Lectures on Anomalies
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• New and old N=8 superconformal field theories in three dimensions
• Semi-Direct Gauge Mediation with the 4-1 Model
• IR Free or Interacting? A Proposed Diagnostic
• On the ISS model of dynamical SUSY breaking
• Comments on Anomalies and Charges of Toric-Quiver Duals
• Landscape of Simple Superconformal Field Theories in 4d
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• Scale invariance vs conformal invariance
• Supersymmetric index on T^2 x S^2 and elliptic genus
• Infrared enhancement of supersymmetry in four dimensions
• ABCD of 3d $\mathcal{N}=8$ and 4 Superconformal Field Theories
• A lattice study of N=2 Landau-Ginzburg model using a Nicolai map
• Scaling dimensions of Coulomb branch operators of 4d N=2 superconformal field theories
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• Pouliot Type Duality via a-Maximization
• A note on $\mathcal{N}\ge 6$ Superconformal Quantum Field Theories in three dimensions
• Deformations of $W_{A,D,E}$ SCFTs
• Kazama-Suzuki models and BPS domain wall junctions in N=1 SU(n) Super Yang-Mills
• Supersymmetric N=1 Spin(10) Gauge Theory with Two Spinors via a-Maximization
• Numerical simulation of the $\mathcal{N}=(2,2)$ Landau-Ginzburg model
• N=1 Supersymmetric $SU(2{)}^r$ Moose Theories
• N=1 Duality and the Superconformal Index
• Exceptional N=1 Duality
• Equivalence of A-Maximization and Volume Minimization
• Numerical study of the $\mathcal{N}=2$ Landau--Ginzburg model
• BLG theories at low values of Chern-Simons coupling

Cited by in corpus (5)

• New 2d $\mathcal{N}=(0,2)$ dualities from four dimensions
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Continuum limit in numerical simulations of the $\mathcal{N}=2$ Landau--Ginzburg model
• Discrete Anomaly Matching for the Pouliot Type Dualities
• Aspects of 4d supersymmetric dynamics and geometry