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MAT752
Advanced Topics in Field Theory
Zeiten:
Organisiert von
- 24.09.2025, 13:15–14:00, Konstantin Wernli
Towards Holography in the BV-BFV formalism
One can place a BV theory on a cylinder I x Sigma and, under some assumptions, integrate out the modes along the cylinder to obtain an effective theory along Sigma. This theory depends on the choice of a polarization, and couples to the boundary conditions. I will briefly recall the setup and some older examples published in joint work with Schiavina, Mnev, and Cattaneo. Then I will discuss recent work with Cabrera and Cueca to apply this to split Chern-Simons theory with topological boundary conditions, where one recovers the Poisson Sigma Model for the Poisson-Lie group integrating the Lie bialgebra. I will comment on possible applications, and generalizations, of this observation.
- 24.09.2025, 14:15–15:00, Timon Leupp
Representations of the Quantized Corner Algebra in 4 Dimensional BF Theory
The quantum BV-BFV framework has become an indispensable tool to perturbatively quantize gauge theories on manifolds with boundaries. It is also possible to extend the formalism to manifolds with corners, to which the QFT assigns an algebra. This corner algebra classifies state spaces and enables a cutting and gluing formula which can reduce the complexity of calculations tremendously and provide new structural insight into the theory.
In this talk, I will present some recent results about representations of the corner algebra in 4-dim. BF theory that were obtained in my Master‘s thesis. At the end, I will mention remaining problems and give an outlook on future projects.
- 01.10.2025, 13:15–15:00, Shuan Jiang
Jet Spaces and Global AKSZ Theories
In this talk, we introduce the notions of jet spaces and, more generally, Costello spaces of dg manifolds, along with their shifted symplectic structures. We then promote the mapping space between dg manifolds to a derived Costello stack. These results provide a natural framework for globalizing AKSZ theories over their moduli spaces of classical solutions. This talk is based on joint work in progress with Alberto Cattaneo.
- 08.10.2025, 13:15–15:00, Manuel Tecchiolli
Gravity on Manifolds with Codimension-1 and Codimension-2 Strata
The Palatini–Cartan theory provides a natural framework to study gravity on manifolds with boundary. A subtler issue arises, however, when the boundary is not the only stratum of the manifold, namely, when the theory descends to codimension-2 corners. In this talk, we will construct the geometry of Palatini–Cartan gravity in the presence of a possibly degenerate boundary metric, and examine the structures induced at the corner. The resulting framework shows a geometric picture that exhibits features reminiscent of a Dirac structure, after some possible reduction on the space of corner fields.
- 15.10.2025, 13:15–15:00, Leon Menger
A 1-dimensional Model for Chern–Simons Theory
In this talk we will explore a 1-dimensional theory on graphs that reproduces the terms of the perturbative Chern–Simons partition function. To warm up, we will briefly review Losev's HTQM [2301.01390], which generalises the notion of a TQFT and provides a general guideline for our theory in one dimension.
Inspired by this we will find that a 1D AKSZ theory coupled to 1D supergravity in the BV-BFV formalism yields a geometric realisation of 1D HTQM on intervals. To be able to reproduce Chern–Simons theory, we will see how interaction vertices (in our case Lie brackets) can be modelled as geometric objects which prescribe gluing laws for the partition functions on several edges.
Finally we will combine the ingredients to define a theory on graphs and obtain the perturbative Chern–Simons partition function in a particular gauge. If time permits, I will also sketch some ideas on how this work relates to a claim by Witten that Chern–Simons theory is a string field theory.
- 12.10.2025, 13:15–15:00, Leon Menger; Filippo Fila-Robattino
- 05.11.2025, 13:15–15:00, Kasia Rejzner
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