Generalized Symmetries and Phases of Gauge Theory (1/4)

• Thomas DUMITRESCU (UCLA)

Room: Marilyn and James Simons Conference Center These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.

Gong show 1 Room: Marilyn and James Simons Conference Center

Introduction to anomalies in condensed matter physics (1/4)

• Max METLITSKI (MIT)

Room: Marilyn and James Simons Conference Center 1) General "definition" of topological phases and of invertible phases. 2) Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion). 3) Introduction of bordism invariance and classification of invertible phases. 4) If time allows, invertible phases with Z classification (Chern simons response) as illustrated by 2+1d p+ip superconductor. 5) Phases protected by symmetry. Symmetry on the lattice. 6) In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.

Speed-dating / Exercices Room: Marilyn and James Simons Conference Center

Generalized Symmetries and Phases of Gauge Theory (2/4)

• Thomas DUMITRESCU (UCLA)

Room: Marilyn and James Simons Conference Center These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.

Introduction to anomalies in condensed matter physics (2/4)

• Max METLITSKI (MIT)

Room: Marilyn and James Simons Conference Center 1) General "definition" of topological phases and of invertible phases. 2) Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion). 3) Introduction of bordism invariance and classification of invertible phases. 4) If time allows, invertible phases with Z classification (Chern simons response) as illustrated by 2+1d p+ip superconductor. 5) Phases protected by symmetry. Symmetry on the lattice. 6) In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.

Generalized Symmetries and Phases of Gauge Theory (3/4)

• Thomas DUMITRESCU (UCLA)

Room: Marilyn and James Simons Conference Center These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.

Exercices Room: Marilyn and James Simons Conference Center

Generalized Symmetries and Phases of Gauge Theory (4/4)

• Thomas DUMITRESCU (UCLA)

Room: Marilyn and James Simons Conference Center These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.

Introduction to anomalies in condensed matter physics (3/4)

• Max METLITSKI (MIT)

Room: Marilyn and James Simons Conference Center 1) General "definition" of topological phases and of invertible phases. 2) Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion). 3) Introduction of bordism invariance and classification of invertible phases. 4) If time allows, invertible phases with Z classification (Chern simons response) as illustrated by 2+1d p+ip superconductor. 5) Phases protected by symmetry. Symmetry on the lattice. 6) In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.

Introduction to anomalies in condensed matter physics (4/4)

• Max METLITSKI (MIT)

Room: Marilyn and James Simons Conference Center 1) General "definition" of topological phases and of invertible phases. 2) Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion). 3) Introduction of bordism invariance and classification of invertible phases. 4) If time allows, invertible phases with Z classification (Chern simons response) as illustrated by 2+1d p+ip superconductor. 5) Phases protected by symmetry. Symmetry on the lattice. 6) In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.

Higher Symmetry in Particle Physics (1/4)

• Clay CÓRDOVA (University of Chicago)

Room: Marilyn and James Simons Conference Center These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.

Higher Symmetry in Particle Physics (2/4)

• Clay CÓRDOVA (University of Chicago)

Room: Marilyn and James Simons Conference Center These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.

Exercices Room: Marilyn and James Simons Conference Center

Higher Symmetry in Particle Physics (3/4)

• Clay CÓRDOVA (University of Chicago)

Room: Marilyn and James Simons Conference Center These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.

Gong Show 2 Room: Marilyn and James Simons Conference Center

Higher Symmetry in Particle Physics (4/4)

• Clay CÓRDOVA (University of Chicago)

Room: Marilyn and James Simons Conference Center These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.

Exercices Room: Marilyn and James Simons Conference Center

Non-Invertible Symmetries (1/3)

• Shu-Heng SHAO (Stony Brook University)

Room: Marilyn and James Simons Conference Center I will review aspects of non-invertible symmetries and their relations to anomalies on the lattice. I will start with the Kramers-Wannier symmetry in the quantum Ising lattice model, and discuss its dynamical consequences. I will then discuss topological phases protected by non-invertible symmetries, with the cluster model as the simplest example.

Generalized Symmetries and their Gauging in 2d CFTs (1/4)

• Yifan WANG (New York University)

Room: Marilyn and James Simons Conference Center After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.

Nonrelativistic Conformal Field Theory (1/2)

• Đàm Thanh SƠN (Univ. of Chicago)

Room: Marilyn and James Simons Conference Center We will review the notions of Schrödinger symmetry and nonrelativistic conformal field theory, in particular the restrictions that Schrödinger symmetry imposes on correlation function and the operator-state correspondence. We will then consider the most important example of NRCFT --- fermions at unitarity, and derive physical consequences of the formalism.

Exercices Room: Marilyn and James Simons Conference Center

Non-Invertible Symmetries (2/3)

• Shu-Heng SHAO (Stony Brook University)

Room: Marilyn and James Simons Conference Center I will review aspects of non-invertible symmetries and their relations to anomalies on the lattice. I will start with the Kramers-Wannier symmetry in the quantum Ising lattice model, and discuss its dynamical consequences. I will then discuss topological phases protected by non-invertible symmetries, with the cluster model as the simplest example.

Generalized Symmetries and their Gauging in 2d CFTs (2/4)

• Yifan WANG (New York University)

Room: Marilyn and James Simons Conference Center After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.

String Theory, Symmetries and Anomalies (1/4)

• Iñaki GARCÍA ETXEBARRIA (Durham University)

Room: Marilyn and James Simons Conference Center I will review some aspects of anomalies of d-dimensional QFTs from a modern viewpoint (in terms of a d+1 dimensional anomaly theory, the "anomaly theory"), how symmetries can be described in a related way in terms of a d+1 dimensional topological field theory (the "SymTFT") and how these d+1 theories arise from string theory.

Exercices Room: Marilyn and James Simons Conference Center

String Theory, Symmetries and Anomalies (2/4)

• Iñaki GARCÍA ETXEBARRIA (Durham University)

Room: Marilyn and James Simons Conference Center I will review some aspects of anomalies of d-dimensional QFTs from a modern viewpoint (in terms of a d+1 dimensional anomaly theory, the "anomaly theory"), how symmetries can be described in a related way in terms of a d+1 dimensional topological field theory (the "SymTFT") and how these d+1 theories arise from string theory.

Non-Invertible Symmetries (3/3)

• Shu-Heng SHAO (Stony Brook University)

Room: Marilyn and James Simons Conference Center I will review aspects of non-invertible symmetries and their relations to anomalies on the lattice. I will start with the Kramers-Wannier symmetry in the quantum Ising lattice model, and discuss its dynamical consequences. I will then discuss topological phases protected by non-invertible symmetries, with the cluster model as the simplest example.

Participant Seminars Room: Marilyn and James Simons Conference Center

Participant Seminars Room: Marilyn and James Simons Conference Center

Generalized Symmetries and their Gauging in 2d CFTs (3/4)

• Yifan WANG (New York University)

Room: Marilyn and James Simons Conference Center After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.

String Theory, Symmetries and Anomalies (3/4)

• Iñaki GARCÍA ETXEBARRIA (Durham University)

Room: Marilyn and James Simons Conference Center I will review some aspects of anomalies of d-dimensional QFTs from a modern viewpoint (in terms of a d+1 dimensional anomaly theory, the "anomaly theory"), how symmetries can be described in a related way in terms of a d+1 dimensional topological field theory (the "SymTFT") and how these d+1 theories arise from string theory.

Nonrelativistic Conformal Field Theory (2/2)

• Đàm Thanh SƠN (Univ. of Chicago)

Room: Marilyn and James Simons Conference Center We will review the notions of Schrödinger symmetry and nonrelativistic conformal field theory, in particular the restrictions that Schrödinger symmetry imposes on correlation function and the operator-state correspondence. We will then consider the most important example of NRCFT --- fermions at unitarity, and derive physical consequences of the formalism.

Exercices Room: Marilyn and James Simons Conference Center

Generalized Symmetries and their Gauging in 2d CFTs (4/4)

• Yifan WANG (New York University)

Room: Marilyn and James Simons Conference Center After a brief review of 2d CFT basics, we introduce generalized, non-invertible symmetries in terms of explicit CFT observables. We describe how such symmetries are formalized by fusion categories and how to implement gauging of such symmetries. We also discuss the physical consequences of these mathematical structures.

Non-Invertible Symmetries in One-Dimensional Quantum Lattice Models

• Clément DELCAMP (IHES)

Room: Marilyn and James Simons Conference Center We will study a lattice realisation of the Symmetry Topological Field Theory (SymTFT) picture for one-dimensional quantum models. We will exploit this picture to study lattice models with non-invertible symmetries, discuss generalised gauging, and construct renormalisation group fixed points of gapped symmetric phases.

String Theory, Symmetries and Anomalies (4/4)

• Iñaki GARCÍA ETXEBARRIA (Durham University)

Room: Marilyn and James Simons Conference Center I will review some aspects of anomalies of d-dimensional QFTs from a modern viewpoint (in terms of a d+1 dimensional anomaly theory, the "anomaly theory"), how symmetries can be described in a related way in terms of a d+1 dimensional topological field theory (the "SymTFT") and how these d+1 theories arise from string theory.