Twisted QFT

This series ran in Spring 2021. For current information on the future of the seminar please email me!


The goal of this lecture series is to examine twists of quantum field theories in low dimensions, focusing on algebraic and homological aspects and the relation between the Batalin-Vilkovisky formalism and more traditional physical approaches (SUSY, superspace, and such). Some beautiful old things and some exciting new things.


The series is organized by Tudor Dimofte and Brian Williams. We send out weekly emails with announcements containing zoom links to the seminar. Contact either of us if you would like to be added to the email list.


On this website we will post slides and video from the lectures.


Here are some partial notes that will be periodically updated. (Notes by Brian, so no blame for inaccuracies should be placed on Tudor.) For supplementary material check out this lecture series on twists of supersymmetric Yang--Mills in the BV formalism.


Here is a list of problems that go along with the lectures.


Problem Set 1 (Based on weeks 2 and 3).


Week 1: Introduction. Zero-dimensional path integrals. Gaussian integrals, the finite dimensional BV formalism, 0d bosons.

Week 2: Fun with gradings and fermions. The 0d BV formalism.

Week 3: BV integration and gauge theory. Localization in 0d SUSY.

Week 4: 0d N=2 supersymmetry in superspace. Symmetries in the BV formalism.

Week 5: Introduction to (classical) mechanics. One-dimensional field theory.

Week 6: Quantum mechanics and the Weyl algebra. Introducing (quantum) local operators and factorization algebras.

Week 7: Quantum mechanics and the Weyl algebra, part II. Circle partition function.

Week 8: Intro to susy. Homotopical regularization.

Week 9: SUSY QM and topological QM.

Week 10: Superspace, A-roof genus from `B-type' topological QM.

Week 11: A-twist topological QM. QM on closed intervals, boundary conditions.

Week 12: B-twisted topological QM, flavor symmetry, and the partition function.