From Polygons to Instantons: A Journey through Gauge Theory

by Prof. Nikita Nekrasov

Thursday 12 Nov 2026, 15:15 → 16:15 Europe/Stockholm

What can a flexible polygon teach us about quantum fields? I will begin with closed polygons in three-dimensional space and their bending motions, showing how their geometry emerges from a two-dimensional gauge theory. Extending this construction leads to polygons in geometries containing cosmic strings and beads, and to gauge theories on “origami” worldsheets.

These elementary pictures open a path to many-body systems and gauge theories in higher dimensions. Passing from two-dimensional Yang–Mills theory to three-dimensional Chern–Simons theory brings spherical geometry and braiding into the story. In four-dimensional supersymmetric gauge theories, instanton partition functions connect to the same geometric structures: in a suitable limit, their logarithms become generating functions for distinguished Lagrangian subspaces of classical phase spaces.

The talk will combine familiar ideas with unpublished work, emphasizing pictures, examples, and the connections between dimensions. No specialist knowledge of gauge theory will be assumed.