### Info

This seminar features recent results at the intersection of high-energy physics, string theory, and geometry and topology.

** Prerequisites:** None. Everyone is welcome. To receive announcements for
this seminar, and for the advertisement of other talks at the intersection of physics and
geometry in Heidelberg,
you may subscribe to the
Mailing List.

** Time and Place:** Regularly: Monday, 2 p.m.s.t., MATHEMATIKON
SR 3

Alternatively: Tuesday or Thursday, 2 p.m.s.t., various locations (or as noted below).

** Online seminar:** During the coronavirus crisis the seminar is held online in cooperation with
LMU Munich
and
University of Vienna.
Please contact the organizers by e-mail to receive the link to the online seminar.

Standard time in the Winter 2020/21 is Monday, 3 p.m.c.t., unless indicated otherwise.

### Online Schedule

Date | Speaker | Title, Abstract | Comments |
---|---|---|---|

October 12 (Starts at 2:30!) |
Ezra Getzler (Northwestern) | Gluing local gauge conditions in BV quantum field theory | Slides |

In supersymmetric sigma models, there is frequently no global choice of Lagrangian submanifold for BV quantization. I will take the superparticle, a toy version of the Green-Schwarz superstring, as my example, and show how to extend the light-cone gauge to the physically relevant part of phase space. This involves extending a formula of Mikhalkov and A. Schwarz that generalizes the prescription of Batalin and Vilkovisky for the construction of the functional integral. This is joint work with S. Pohorence | |||

October 19 | Christopher Beem (Oxford) | Hall-Littlewood Chiral Rings and Derived Higgs Branches | |

I will discuss a relatively novel algebraic structure arising in four-dimensional N=2 superconformal field theories: the Hall-Littlewood Chiral Ring. The HLCR is in a refinement of the more familiar Higgs branch chiral ring which encodes the Higgs branch of the moduli space of vacua as an algebraic variety. The HLCR in gauge theories is constructed as the cohomology of a kind of BRST complex, which allows it to be identified with the ring of functions on the derived Higgs branch (in the sense of derived algebraic geometry). I will describe the solution of the HLCR cohomology problem for a large class of Lagrangian theories (the class S theories of type A1), which illustrate a number of key features. | |||

October 26 | Theo Johnson-Freyd (Dalhousie) | 3+1d topological orders with (only) an emergent fermion | |

There are exactly two bosonic 3+1d topological orders whose only nontrivial quasiparticle is an emergent fermion (and exactly one whose only nontrivial quasiparticle is an emergent boson). I will explain the meaning of this sentence: I will explain what a "3+1d topological order" is, and how I know that these are the complete list. Time permitting, I will you some details about these specific topological orders, and say what this classification has to do with "minimal modular extensions". | |||

November 2 | Matthias Traube (LMU - München) | Cardy Algebras, Sewing-Constraints and String-Nets | |

In this talk I will bring together three different concepts surrounding categorial description for RCFTs. Firstly, Cardy algebras were introduced by Kong in order to describe the genus zero and one part of full open-closed RCFTs. Secondly, string-nets were shown by Kirillov to compute the state of the Reshetikhin-Turaev three dimensional topological field theory. I will bring the two ingredients together, in order to show the third one. That is, I will show how Cardy algebra colored string-nets solve the sewing constraints, thereby giving rise to consistent correlators in full open-close RCFTs and vice versa. The talk is based on the preprint: arXiv:2009.11895. | |||

November 9 | Ilka Brunner (LMU - München) | Flow Defects and Phases of gauged linear sigma models | |

I will discuss a special class of defects in two dimensional supersymmetric theories. These "flow defects" connect UV and IR theories. They can in particular be used in the context of gauged linear sigma models, where they connect different phases. Here, they can be regarded as functors between brane categories and provide a new point of view on the "grade restriction rule" initially proposed by Herbst, Hori and Page. | |||

November 16 | Owen Gwilliam (Amherst) | Centers of higher enveloping algebras and bulk-boundary systems | |

The universal enveloping algebra of a Lie algebra plays a key role in representation theory (for obvious reasons) and in physics, particularly in encoding symmetries of quantum systems. But it is just one in a family of higher enveloping algebras: each dg Lie algebra g has an enveloping E_n algebra U_n(g). (Here E_n refers to "n-dimensional algebras" in the sense of the little n-disks operad.) This construction admits a nice presentation via factorization algebras, by work of Knudsen, and we will discuss how it relates to symmetries of quantum field theories. We will discuss a model for the *center* of U_n(g) and how this framework encodes the observables of a bulk-boundary system where the bulk is topological BF theory for Lie algebra g and the boundary encodes "topological currents." (This is joint work with Greg Ginot, Brian Williams, and Mahmoud Zeinalian.) | |||

November 30 | Jörg Teschner (Universität Hamburg / Desy) | Proposal for a Geometric Characterisation of Topological String Partition Functions | |

We propose a geometric characterisation of the topological string partition functions associated to the local Calabi-Yau (CY) manifolds used in the geometric engineering of d = 4, N = 2 supersymmetric field theories of class S. A quantisation of these CY manifolds defines differential operators called quantum curves. The partition functions are extracted from the isomonodromic tau-functions associated to the quantum curves by expansions of generalised theta series type. It turns out that the partition functions are in one-to-one correspondence with preferred coordinates on the moduli spaces of quantum curves defined using the Exact WKB method. The coordinates defined in this way jump across certain loci in the moduli space. The changes of normalisation of the tau-functions associated to these jumps define a natural line bundle. | |||

December 7 | Susanne Reffert (Universität Bern) | The Large Charge Expansion | |

It has become clear in recent years that working in sectors of large global charge of strongly coupled and otherwise inaccessible CFTs leads to important simplifications. It is indeed possible to formulate an effective action in which the large charge appears as a control parameter. In this talk, I will explain the basic notions of the large-charge expansion using the simple example of the O(2) model and then generalize to the non-Abelian case which has a richer structure and exhibits new effects. | |||

December 14 | Dmitri Bykov (LMU - Munchen) | Sigma models as Gross-Neveu models | |

I will show that there is a wide class of integrable sigma models, which includes CP^{n-1}, Grassmannian, flag manifold models, that are equivalent to bosonic (and mixed bosonic/fermionic) chiral Gross-Neveu models. The established equivalence allows to effortlessly construct trigonometric/elliptic deformations, provides a new look on the supersymmetric theory and on the cancellation of anomalies in the integrability charges. Using this formalism, we develop criteria for constructing quantum integrable models related to quiver varieties. Based on arXiv:2006.14124 and arXiv:2009.04608. | |||

January 11 | Kasia Rejzner (University of York) | BV-BFV formalism in perturbative AQFT | |

BV-BFV formalism is a general framework for quantising gauge theories on manifolds with boundary. In this talk I will present some ideas on how to incorporate this framework into perturbative algebraic quantum field theory (pAQFT), which is a mathematically rigorous approach to QFT. After discussing general ideas, I will focus on their application to the study of asymptotic structure of quantum electrodynamics. |

### Organizers

Prof. J. Walcher, walcher@uni-heidelberg.de

Dr. Simone Noja,
noja@mathi.uni-heidelberg.de