Higher Gauge Theory and Integrability
演讲者
Joaquin Liniado
时间
2025年05月06日 09:45 至 11:30
地点
A3-1-103
线上
Zoom 468 248 1222
(BIMSA)
摘要
Integrable field theories are remarkable for possessing an infinite number of conserved quantities, which often allow for their exact solvability. In two dimensions, this structure is elegantly captured by the existence of a Lax connection, whose path ordered exponential allows for the systematic construction of an infinite number of conserved quantities. Recently, Witten, Costello, and Yamazaki, provided a gauge-theoretic origin for the Lax connection via a four-dimensional variant of Chern–Simons theory.
A natural question is how to extend this perspective to three dimensions. In this talk, I will argue that the appropriate generalization involves surface observables, from which one can extract an infinite number of conserved quantities. Motivated by the CWY framework, in collaboration with Hank Chen, we develop a higher gauge-theoretic construction based on a categorified version of Chern–Simons theory in five dimensions, which gives a natural origin for these surface holonomies.
A natural question is how to extend this perspective to three dimensions. In this talk, I will argue that the appropriate generalization involves surface observables, from which one can extract an infinite number of conserved quantities. Motivated by the CWY framework, in collaboration with Hank Chen, we develop a higher gauge-theoretic construction based on a categorified version of Chern–Simons theory in five dimensions, which gives a natural origin for these surface holonomies.