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Topological Gauge theories and integrable models

Grant number: 19/12167-3
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): August 01, 2019
Effective date (End): February 28, 2023
Field of knowledge:Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
Principal researcher:Pedro Gil Martins Vieira
Grantee:Matheus Augusto Fabri
Home Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil
Associated research grant:16/01343-7 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics, AP.TEM

Abstract

This project has as its primal objective to extend the recent developments that topological gauge theories are connected with integrable models. These are based on a topological field theory of Schwartz type that has a four dimensional Chern-Simons type action with complex gauge group G defined on a product manifold that consists of a topological plane times a holomorphic manifold. The idea is that the projections of crossings of Wilson lines in this gauge theory can be interpreted as R-matrices of a integrable model with symmetry group G lying in the topological plane with the coordinate in the holomorphic manifold being the spectral parameter of the R-matrix. Then using this formalism we hope to shed light in the classification of integrable models, in how the fusion rules arise in this framework and more importantly how a duality dictionary can be build relating topological gauge theories in higher dimensions with integrable models in lower dimensions like a holographic principle. (AU)

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