Graph potentials and topological quantum field theories
Algebraic Geometry
2023-10-12 v2 Mathematical Physics
Geometric Topology
math.MP
Quantum Algebra
Abstract
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. We show that the birational type of the graph potential only depends on the homotopy type of the colored graph, and use this to define a topological quantum field theory. A similar construction was recently introduced independently by Kontsevich--Odesskii under the name of multiplicative kernels. We end our paper by giving an efficient computational method to compute its partition function. This is the first paper in a series, and we give a survey of the applications of graph potentials in the other parts.
Keywords
Cite
@article{arxiv.2205.07244,
title = {Graph potentials and topological quantum field theories},
author = {Pieter Belmans and Sergey Galkin and Swarnava Mukhopadhyay},
journal= {arXiv preprint arXiv:2205.07244},
year = {2023}
}
Comments
35 pages, improved exposition and included comparison to recent work of Kontsevich-Odesskii; split off from arXiv:2009.05568v2