Geometry and String Theory
Fall 2015

This is the homepage for the UT Geometry and String Theory Seminar. At the organizational meeting we will flesh out the details of our plans for the semester. Below are some suggestions to get us started.

Fall 2015 Schedule

Date	Speaker	Topic
8/26		Organizational Meeting
9/2	Valentin Zakharevich	Kitaev’s Toric Code
9/9	Behzat Ergun, Daniel Allcock	Intro to CFT I
9/16	David Simmons-Duffin	TBA
9/23	—	—
9/30	Behzat Ergun, Daniel Allcock	Intro to CFT II
10/7	David Ben Zvi	Unitary Irreps of the Conformal Algebra
10/14	Dan Freed	Invariants of Dirac Operators
10/21	Sam Gunningham	Fermions and Topological Phases (Witten)
10/28	Michele Del Zotto	TBA
11/4	Andy Neitzke	Unitary Irreps of the Superconformal Algebra
11/11	Fei Yan	The Superconformal Index
11/18	Jacques Distler	Trace Anomalies and 6D SCFT
12/2	Lorenzo Sadun	Integer Quantum Hall Effect

References

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”

$(1,0)$ 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

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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