The mathematics of supersymmetric lattice models and supersymmetric quantum field theories

Project funded by Swedish Research Council (Project grant), grant 2015-05201_VR. Participating organisations named by the source: Chalmers University of Technology. Funded amount: SEK 3,200,000, as stated by the source. Runs 2016-01-01 to 2019-12-31. Keywords: Naturvetenskap, Natural Sciences, Matematik, Mathematics, Matematisk analys, Mathematical Analysis. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2025-12-06); national funding data, not CORDIS. Abstract given by the source: The aim of the project is to explore novel connections between several different areas of mathematics, including branches of algebra, analysis, combinatorics and mathematical physics. In particular, we will study mathematical properties of elliptic lattice models in statistical mechanics, such as the eight-vertex and 8VSOS model, the three-colour model and the XYZ spin chain. We have recently shown that special polynomials related in various ways to these models can be identified with tau functions of Painlevé VI and with specialized affine Lie algebra characters. In the proposed project, we will exploit these novel relations, which lay the mathematical foundation for understanding the combinatorics of elliptic lattice models. In the spirit of the Cantini-Sportiello theorem, we will relate eigenvectors of the supersymmetric XYZ Hamiltonian to the combinatorics of three-colourings. We will find new relations between affine Lie algebra characters and symmetry classes of three-colourings of a chessboard. We will also investigate the large lattice limit of the three-colour model with domain wall boundary conditions. In particular, we plan to rigorously prove our conjectured expression for the free energy, and investigate macroscopic boundary effects. We also hope to use related methods to study two-point correlation functions and the magnetic susceptibility for the Ising model on the square lattice. Finally, we will rigorously prove new and conjectured properties of superconformal indices for three- and four-dimensional quantum field theories, which mathematically take the form of identities for basic and elliptic hypergeometric integrals. This gives a method for checking dualities between different theories, and for discussing new dualities and hidden symmetries of such theories.

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Swedish Research Council. Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project, funded by the Swedish Research Council with SEK 3,200,000, runs from 2016 to 2019 at Chalmers University of Technology. It aims to explore connections in mathematics related to elliptic lattice models and their properties. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.