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MAT752
Advanced Topics in Field Theory
Zeiten:
Organized by
- 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, 13:15–14:00, Filippo Fila-Robattino
The reduced corner Dirac structure of first order gravity
Classical field theories on stratified manifolds present several geometric and algebraic structures. Starting from the study of constraints on the space of boundary fields, assuming non-empty coners, one can inducethe data of a distribution on the standard Courant algebroid on the space of corner fields.
In this talk I will show that, in the case of Palatini-Cartan gravity in 4D, upon choosing appropriate constraints, the induced distribution on the space of corner fields is involutive and isotropic.
Furthermore I will show that, after reduction of the space of corner fields, such distribution descends to a Dirac structure, which can additionally be obtained as the graph of a Poisson bivector.
- 12.10.2025, 14:15–15:00, Leon Menger
Reduction of 1D SUGRA
We will go over some details of the reduction techniques for bulk and boundary fields of 1-dimensional SUGRA in the BV-BFV formalism.
- 05.11.2025, 13:15–15:00, Pavel Mnev
Globalization of Chern-Simons theory on the moduli space of flat connections
Path integral of Chern-Simons theory on a closed 3-manifold gives a family of perturbative partition functions (effective BV actions induced on twisted de Rham cohomology) parametrized by the moduli space of flat connections. This family is horizontal with respect to the Grothendieck connection modulo a BV-exact term. I will outline how
(a) this family can be extended to a nonhomogeneous form over triples (kinetic flat connection, gauge-fixing flat connection, metric), satisfying a differential quantum master equation (i.e., is annihilated by an appropriate “Gauss-Manin” flat superconnection);
(b) one extract from the extended partition function above a volume form on the smooth irreducible stratum of moduli space, whose cohomology class is metric-independent, and hence yields an invariant of a framed 3-manifold.
The talk is based on a joint work with Konstantin Wernli, arXiv:2510.18653 [math-ph].
- 12.11.2025, 13:15–15:00, Alberto Cattaneo
BV pushforward and applications
After recalling the basics of BV integration and BV pushforward, I will outline some applications: derivation of some physical theories from topological theories; the construction of surface observables for BF_4 and the related 2-knot invariants; the construction of electric flux observables in nonabelian YM_4.
- 19.11.2025, 13:15–15:00, Orev Malatesta
Gravity and BF Theory Equivalence in 3 Dimensions
In this talk we will review the Palatini–Cartan formulation of gravity and focus on its special features in three dimensions, where gravity admits a topological description. We will describe the correspondence between 3-dimensional gravity and BF theory: their classical field content and gauge symmetries. Building on this, we will present the BV formulations of both theories and construct an explicit symplectomorphism between them, thereby establishing their strong equivalence.
- 26.11.2025, 13:15–14:00, Raffaele Lormartire
D-modules in field theory
I will review some aspects of D-module theory and their use in (classical) field theory. Then, I will sketch possible approaches to generalizations to manifolds with boundary and nonlinear differential operators.
- 26.11.2025, 14:15–15:00, Florian Aggias
Costello proposed a method of homotopic renormalization for quantum BV theories. After recalling some elements of functional analysis, I will give an introduction to homotopic renormalization. Further, I will discuss the application of this method to Yang-Mills theory coupled to spinor fields on 4-dim. Euclidean space. This results in the renormalizability of Yang-Mills-Dirac theory on 4-dim. Euclidean space, as well as a classification of deformations and symmetries of the action, as obtained in my Master's thesis.
- 10.12.2025, 13:15–14:00, Alberto Cattaneo
BV pushforward and applications II
I will discuss the construction of surface observables for BF_4, the related 2-knot invariants, and the construction of electric flux observables in nonabelian YM_4.
- 10.12.2025, 14:15–15:00, Giovanni Mocellin
The Cartan Calculus on the infinite jet bundle
Sati and Giotopoulos proposed a categorical setting for formalizing the variational calculus of Bosonic Lagrangian field theories. In this talk, I will present, after introducing their category, how this framework naturally formalizes the Cartan calculus on the infinite jet bundle by restricting to globally finite-order differential forms.
- 17.12.2025, 13:15–15:00, Pavel Mnev
Observables of the form delta(field)
In field theories in the functional integral one often has to deal with the problem of zero-modes. One way is to integrate out the complement of zero-modes, thereby constructing the effective action. The other way is to include a special “zero-mode soaking” observable. We will focus on this latter approach. For a scalar field the observable takes the form delta(phi). I will show examples of such observables in the context of conformal and topological field theory. E.g., in bosonic string theory the presence of such observable is responsible for the “ghost number anomaly” 3*(1-genus). In a (bosonic) 2d beta-gamma system, the correlator of a collection of delta-observables is expressed, surprisingly, as the inverse of the sum of Wick contractions.
Standard|
- 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, 13:15–14:00, Filippo Fila-Robattino
The reduced corner Dirac structure of first order gravity
Classical field theories on stratified manifolds present several geometric and algebraic structures. Starting from the study of constraints on the space of boundary fields, assuming non-empty coners, one can inducethe data of a distribution on the standard Courant algebroid on the space of corner fields.
In this talk I will show that, in the case of Palatini-Cartan gravity in 4D, upon choosing appropriate constraints, the induced distribution on the space of corner fields is involutive and isotropic.
Furthermore I will show that, after reduction of the space of corner fields, such distribution descends to a Dirac structure, which can additionally be obtained as the graph of a Poisson bivector.
- 12.10.2025, 14:15–15:00, Leon Menger
Reduction of 1D SUGRA
We will go over some details of the reduction techniques for bulk and boundary fields of 1-dimensional SUGRA in the BV-BFV formalism.
- 05.11.2025, 13:15–15:00, Pavel Mnev
Globalization of Chern-Simons theory on the moduli space of flat connections
Path integral of Chern-Simons theory on a closed 3-manifold gives a family of perturbative partition functions (effective BV actions induced on twisted de Rham cohomology) parametrized by the moduli space of flat connections. This family is horizontal with respect to the Grothendieck connection modulo a BV-exact term. I will outline how
(a) this family can be extended to a nonhomogeneous form over triples (kinetic flat connection, gauge-fixing flat connection, metric), satisfying a differential quantum master equation (i.e., is annihilated by an appropriate “Gauss-Manin” flat superconnection);
(b) one extract from the extended partition function above a volume form on the smooth irreducible stratum of moduli space, whose cohomology class is metric-independent, and hence yields an invariant of a framed 3-manifold.
The talk is based on a joint work with Konstantin Wernli, arXiv:2510.18653 [math-ph].
- 12.11.2025, 13:15–15:00, Alberto Cattaneo
BV pushforward and applications
After recalling the basics of BV integration and BV pushforward, I will outline some applications: derivation of some physical theories from topological theories; the construction of surface observables for BF_4 and the related 2-knot invariants; the construction of electric flux observables in nonabelian YM_4.
- 19.11.2025, 13:15–15:00, Orev Malatesta
Gravity and BF Theory Equivalence in 3 Dimensions
In this talk we will review the Palatini–Cartan formulation of gravity and focus on its special features in three dimensions, where gravity admits a topological description. We will describe the correspondence between 3-dimensional gravity and BF theory: their classical field content and gauge symmetries. Building on this, we will present the BV formulations of both theories and construct an explicit symplectomorphism between them, thereby establishing their strong equivalence.
- 26.11.2025, 13:15–14:00, Raffaele Lormartire
D-modules in field theory
I will review some aspects of D-module theory and their use in (classical) field theory. Then, I will sketch possible approaches to generalizations to manifolds with boundary and nonlinear differential operators.
- 26.11.2025, 14:15–15:00, Florian Aggias
Costello proposed a method of homotopic renormalization for quantum BV theories. After recalling some elements of functional analysis, I will give an introduction to homotopic renormalization. Further, I will discuss the application of this method to Yang-Mills theory coupled to spinor fields on 4-dim. Euclidean space. This results in the renormalizability of Yang-Mills-Dirac theory on 4-dim. Euclidean space, as well as a classification of deformations and symmetries of the action, as obtained in my Master's thesis.
- 10.12.2025, 13:15–14:00, Alberto Cattaneo
BV pushforward and applications II
I will discuss the construction of surface observables for BF_4, the related 2-knot invariants, and the construction of electric flux observables in nonabelian YM_4.
- 10.12.2025, 14:15–15:00, Giovanni Mocellin
The Cartan Calculus on the infinite jet bundle
Sati and Giotopoulos proposed a categorical setting for formalizing the variational calculus of Bosonic Lagrangian field theories. In this talk, I will present, after introducing their category, how this framework naturally formalizes the Cartan calculus on the infinite jet bundle by restricting to globally finite-order differential forms.
- 17.12.2025, 13:15–15:00, Pavel Mnev
Observables of the form delta(field)
In field theories in the functional integral one often has to deal with the problem of zero-modes. One way is to integrate out the complement of zero-modes, thereby constructing the effective action. The other way is to include a special “zero-mode soaking” observable. We will focus on this latter approach. For a scalar field the observable takes the form delta(phi). I will show examples of such observables in the context of conformal and topological field theory. E.g., in bosonic string theory the presence of such observable is responsible for the “ghost number anomaly” 3*(1-genus). In a (bosonic) 2d beta-gamma system, the correlator of a collection of delta-observables is expressed, surprisingly, as the inverse of the sum of Wick contractions.
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Module: MAT752 Advanced Topics in Field Theory