Motives: an introductory survey for physicists

TL;DR

This paper introduces physicists to the accessible aspects of Grothendieck's motives, highlighting recent applications in quantum field theory and exploring connections between motivic theory and physics.

Contribution

It provides an introductory survey of motives tailored for physicists, emphasizing recent interdisciplinary applications and including an appendix on motivic theory's links to physics.

Findings

Motivic theory has emerging applications in quantum field theory

Accessible explanations facilitate physicists' understanding of motives

Connections between motivic theory and physics are expanding

Abstract

We survey certain accessible aspects of Grothendieck's theory of motives in arithmetic algebraic geometry for mathematical physicists, focussing on areas that have recently found applications in quantum field theory. An appendix (by Matilde Marcolli) sketches further connections between motivic theory and theoretical physics.