Instanton in Lattice QCD from Higher Category Theory

ADS seminar

Organizers：

数学物理团队

Speaker：

Jing-Yuan Chen (IASTU)

Time：

Thur., 13:30-15:05, Sept. 26, 2024

Venue：

Qiuzhen Hall, Ningzhai

(Inside Tsinghua main campus)

Title：

Instanton in Lattice QCD from Higher Category Theory

Abstract:

A long standing problem in lattice QCD is to find a natural definition of instanton operator on the lattice. I will show how this problem is -- and has to be -- solved by higher category theory. In this language, the solution is a deep generalization of the Villain model familiar in condensed matter physics and in lattice Maxwell. Using the particular categorical structure, one can define 2d Wess-Zumino-Witten term, 3d skrymion and 4d hedgehog in lattice S^3 (pion) non-linear sigma model, and 3d Chern-Simons term, 4d instanton and 5d Yang monopole in lattice Yang-Mills.

In a larger scope, I will sketch a systematic program towards rethinking the relation between continuum QFT and lattice QFT. As a result, all topological operators can be naturally defined on the lattice. I will discuss what implications this might have on the understanding of renormalization, the relation between dynamical and topological QFT (in particular, going beyond the well-developed tensor category formalism which only deals with discrete degrees of freedom, and find a unifying language that emcompases the more physical continuous degrees of freedom), and the program of constructive QFT.