ZMP Seminar and Colloquium (Winter term 2022/23)

The topic of the ZMP Seminar this term will be Vertex operator algebras and topological field theories from twisted QFTs in 3d and 4d . For questions about the seminar, please contact Sven Möller, Ingo Runkel, Christoph Schweigert or Jörg Teschner.

The seminar and the colloquium will take place in presence. In the Geomatikum we meet in H3, at DESY in seminar room 2. The seminar takes place at 2.15pm and the colloquium at 4.15.

The plan for this term is (subject to change):

It has been known for a while that quantum field theories (QFTs) with extended supersymmetry can be topologically twisted. Another possibility which has attracted a lot of interest more recently are holomorphic twists, rendering the supersymmetric field theories holomorphic rather than topological in part of the spacetime. Variants of this construction can give theories which are topological in the bulk of spacetime, and holomorphic on boundaries, for example. In the cases of three-dimensional and four-dimensional supersymmetric QFTs one can thereby find algebras of holomorphic operators supported on two-dimensional surfaces or boundaries, closely related to mathematical structures familiar from two-dimensional conformal field theories like vertex algebras. Topological-holomorphic twists yield theories expected to generalise the correspondences between VOAs and three-dimensional TQFT intensively studied in the past. On the one hand, this provides access to new computable aspects of gauge theories with extended supersymmetry. On the other hand, these vertex algebras and topological field theories are different from the ones previously studied and provide new important challenges for the field. The relevant structures are generically expected not to be semisimple, and derived and dg-enhanced structures as well as deformations have to be considered.
In this sequence of seminar talks, we plan to address the following topics:
  1. What are topological twists, and which twists are relevant for three- and four-dimensional topological field theories?
  2. What is a vertex algebra, and which vertex algebras are relevant for the 3d/VOA and the 4d/VOA correspondence?
  3. For the 4d/VOA correspondence: relation between the Higgs branch of the supersymmetric Yang-Mills theory and the variety associated to the VOA.
  4. For the 3d/VOA correspondence: relation between categories of line operators and VOA representation categories, and between bulk local operators and the Higgs branch.

Seminar notes:
Some references: