Representation-theoretic interpretation of the Standard Model

The paper considers formal path-integral expressions from quantum field theory, including integration over spaces of connections and spinor fields, and seeks a representation-theoretical interpretation of the quantum field theories appearing in the Standard Model.

Representation-theoretic interpretation conjecture. The quantum field theory of the standard model may be understood purely in terms of the representation theory of the automorphism group of some geometric structure.

The conjecture is the paper's main motivating goal: it proposes that representation theory could provide a mathematical framework for understanding the Standard Model, while also using physical theories to guide the study of representation theory for presently poorly understood infinite-dimensional groups.