# Topological Phases and Relativistic QFTs

## Contents

The main aim is to revisit various known constructions in relativistic QFTs on the hep-th side of the community, from a new viewpoint of the symmetry protected topological phases, introduced by the cond-mat side of the community. The lectures are mostly about 温故知新, i.e. by warming-up the old to learn the new.

A hard-to-read handwritten notes are available. The notes are organized as follows:

- Lecture 1: Perturbative gauge anomalies and the integer quantum Hall effect
- Lecture 2: Projective representations, 0+1d anomalies and 1+1d Dijkgraaf-Witten theory
- Lecture 3: Three generalizations: to higher dimensions, to mixed anomalies, to higher-form symmetries
- Lecture 4: Anomalies and the phase structure of 4d SU(2) pure Yang-Mills at θ=π (based on arXiv:1703.00501 by Gaiotto-Kapustin-Komargodski-Seiberg)
- Lecture 5: Kramers-Wannier, Jordan-Wigner and GSO projection via 2+1d TQFT

Four hours at the CERN winter school 2018, on Feb 12-16, 2018, and four and a half hours at Rikkyo University, Feb 28, 2018.

In the actual lectures in CERN, I didn't have time to talk about the higher-form generalizations and the original lecture 4. Instead I prepared the lecture 5 in the morning of the last day and gave a talk on it instead.

The video recordings at CERN are available below:
Lecture 1,
Lecture 2,
Lecture 3,
Lecture 4

email: yuji.tachikawa_at_****.**