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):
Abstract:
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 threedimensional and fourdimensional supersymmetric
QFTs one can thereby find algebras of holomorphic operators supported on
twodimensional surfaces or boundaries, closely related to mathematical structures
familiar from twodimensional conformal field theories like vertex algebras.
Topologicalholomorphic twists yield theories expected to generalise the
correspondences between VOAs and threedimensional 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
dgenhanced structures as well as deformations have to be considered.
In this sequence of seminar talks, we plan to address the following topics:
 What are topological twists, and which twists are relevant for three
and fourdimensional topological field theories?
 What is a vertex algebra, and which vertex algebras are relevant for the
3d/VOA and the 4d/VOA correspondence?
 For the 4d/VOA correspondence: relation between the Higgs branch of the
supersymmetric YangMills theory and the variety associated to the VOA.
 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:
 Associated varieties for vertex algebras:
 4d/VOA correspondence:

Original paper:
C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees,
Infinite Chiral Symmetry in Four Dimensions,
Commun. Math. Phys. 336 (2015) 13591433,
arXiv:1312.5344 [hepth]
 A review:
M. Lemos,
Lectures on chiral algebras of N=2 superconformal field theories,
arXiv:2006.13892 [hepth]
 3d/VOA correspondence:
 Jörg Teschner's introduction on November 3 was based on:
K. Costello, T. Dimofte, D. Gaiotto,
Boundary Chiral Algebras and Holomorphic Twists,
arXiv:2005.00083 [hepth]
 T. Creutzig, T. Dimofte, N. Garner and N. Geer,
A QFT for nonsemisimple TQFT,
arXiv:2112.01559 [hepth]
 (more to come)