YOUNGST@RS - Combinatorics in Fundamental Physics

Session

Combinatorics in Perturbative QFT

Nov 28, 2024, 4:00 PM

Mainz Institute for Theoretical Physics, Johannes Gutenberg University

1. Alessandra Frabetti: Algebraic view on renormalization

11/28/24, 4:00 PM

Renormalization Hopf algebras represent a pro-algebraic group linking the BPHZ and Dyson renormalization formulas, where Feynman graphs are "virtual" coordinates for correlation functions and renormalization factors. In this talk I clarify the mathematical background of this statement and show how it can help improve the BPHZ formula. Time permitting, I also show how this naturally leads to a...

2. Michael Borinsky: Bivariate exponential integrals and edge-bicolored graphs

11/28/24, 4:45 PM

We show that specific exponential bivariate integrals serve as
generating functions of labeled edge-bicolored graphs. Based on this, we
prove an asymptotic formula for the number of regular edge-bicolored
graphs with arbitrary weights assigned to different vertex structures.
The asymptotic behavior is governed by the critical points of a
polynomial. As an application, we discuss the...

9. Simone Hu: Orientation forms on the odd graph complex

11/28/24, 5:20 PM

In this talk we will introduce Kontsevich's odd commutative graph complex and describe a program to detect its non-trivial (co)homology classes via associating convergent integrals to combinatorial graphs, in the spirit of Feynman integrals. In particular, we study closed differential forms constructed using the Pfaffian of skew-symmetric matrices and whose integrals give rise to cocycles in...

10. Johannes Thürigen: Tensor combinatorics in the renormalization group

11/28/24, 5:55 PM

Generalizations of vector field theories to tensors allow to similarly apply large-N techniques but find a richer though often still tractable structure. Generating discrete geometries via their perturbative series, they are furthermore candidates for Quantum Gravity. However, the potential of such tensor theories has not been fully exploited since only a symmetry-reduced ``isotropic'' part...

3. Nathan Pagliaroli: Map enumeration from path integrals over noncommutative geometries

11/28/24, 6:30 PM

In this talk we will explore path integrals over finite spectral triples as models of Euclidean Quantum Gravity, first proposed by J. W. Barrett. Such integrals can be expressed as bi-tracial multi-matrix integrals. The Feynman diagrams of these integrals are decorated maps, and they satisfy their own Schwinger-Dyson equations which are generalizations of Tutte's recursion. I will outline how...