New Perspectives on Theoretical Physics: Representation Theory.

ABSTRACT: In this talk I will describe the relationship between theoretical physics and representation theory (RT). I will introduce many physical concepts (with examples), such as BPS spectra, S-duality, 't Hooft line operators and groups, and relate them to theorems and concepts of RT (such as categories of modules over path algebras, mutation invariance of the derived categoriy of quiver representations, Ginzburg algebras, cluster categories and more).

The main reference for the first part of the talk is [1] .
Afterwards, I will focus on some new results -- current work with
S. Cecotti -- on how to exploit RT to give a full classification
of a class of holomorphic integrable systems (a.k.a.
Supersymmetric Quantum Field Theories). For partial results, refer
to [2].

[1] Matteo
Caorsi and Sergio Cecotti, Categorical Webs and S-duality in 4d N=2
QFT, ArXiv:1707.08981, to appear in Communications
in Mathematical Physics

[2]
Matteo Caorsi and Sergio Cecotti, Special
arithmetic of Flavor, J. High Energ. Phys. (2018)
2018:57