Geometry and String Theory
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Conformal Field Theory Generalities

• Chapters 1-4 of di Francesco, Mathieu and Senechal, “Conformal Field Theory”
• Rychkov, “EPFL Lectures on Conformal Field Theory in $D\geq3$ Dimensions”

Unitary Representations of the (super)Conformal Algebra

• Mack, “All Unitary Ray Representations of the Conformal Group SU(2,2) with Positive Energy,” Com. Math. Phys. 55, 1 (1977).
• Minwalla, “Restrictions imposed by superconformal invariance on quantum field theories”
• Dolan and Osborn, “On short and semi-short representations for four-dimensional superconformal symmetry”

Crossing Symmetry and Conformal Blocks

• Osborn and Petkou, “Implications of conformal invariance in field theories for general dimensions”
• Dolan and Osborn, “Conformal four point functions and the operator product expansion”
• Dolan and Osborn, “Conformal partial waves and the operator product expansion”
• Dolan and Osborn, “Conformal Partial Waves: Further Mathematical Results”

The (super)Conformal Bootstrap

• Rattazzi, Rychkov, Tonni and Vichi, “Bounding scalar operator dimensions in 4D CFT”
• Beem, Lemos, Rastelli, van Rees, “The (2,0) superconformal bootstrap”

The Superconformal Index

• Kinney, Maldacena, Minwalla and Raju, “An Index for 4 dimensional super conformal theories”
• Rastelli and Razamat,“The superconformal index of theories of class $\mathcal{S}$”

Uniqueness of the 6D (2,0) Theories, the a-Theorem and Anomalies

• Cordova, Dumitrescu and Intriligator, “Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories”

• Cordova, Dumitrescu and Intriligator, “Deformations of Superconformal Theories”

$(1,0)$ SCFTs in 6 Dimensions

• J. Heckman, D. Morrison, C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• M. Del Zotto, J. Heckman, A. Tomasiello, C. Vafa, 6d Conformal Matter

Books and Survey Papers: Topological Insulators and Superconductors

• Wen, Quantum Field Theory of Many-Body Systems

• Bernevig, Hughes, Topological Insulators and Topological Superconductors

• Hassan, Kane, Topological insulators

• Qi, Zhang, Topological insulators and superconductors

Kitaev’s Toric Code

• Kitaev, Fault-tolerant quantum computation by anyons

• Freedman, Hastings Double semions in arbitrary dimensions

Classification of Invertible Topological Phases

• Freed, Short-range entanglement and invertible field theories

• Chen, Gu, Liu, Wen, Symmetry protected topological orders and the group cohomology of their symmetry group

• Kapustin, Turzillo, Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases

• Witten, Fermion path integrals and topological phases

• Witten, Lecture at PiTP: slides video

Generalized Global Symmetries

• Gaiotto, Kapustin, Seiberg, Willett, Generalized global symmetries and references therein

• Sharpe, Notes on generalized global symmetries in QFT

Topological Band Theory

• Kane, Topological band theory and the Z/2 invariant

• Kane, Lectures at PiTP

• Freed, Moore, Equivariant topological matter

Integer Quantum Hall Effect

• Witten, Lectures at PiTP, particularly Lecture 2

• Witten, Lecture: The Chern-Simons functional in condensed matter physics

• Wen, Quantum Field Theory of Many-body Systems, Section 4.4

Fractional Quantum Hall Effect

• Read, Moore, Nonabelians in the fractional quantum Hall effect

• Read, Lectures at PiTP, particularly Lecture 2

• Wen, Quantum Field Theory of Many-body Systems, Chapter 7

Superconductivity

• Weinberg, Superconductivity for particular theorists

• Witten, From superconductors and four-manifolds to weak interactions