PIRSA:25090046

Video URL

https://pirsa.org/25090046

Instanton and Chern-Simons in Lattice Yang-Mills Theory from Higher Category Theory

Chen, J. (2025). Instanton and Chern-Simons in Lattice Yang-Mills Theory from Higher Category Theory. Perimeter Institute for Theoretical Physics. https://pirsa.org/25090046

Chen, Jing-Yuan. Instanton and Chern-Simons in Lattice Yang-Mills Theory from Higher Category Theory. Perimeter Institute for Theoretical Physics, Sep. 11, 2025, https://pirsa.org/25090046 

          @misc{ scivideos_PIRSA:25090046,
            doi = {},
            url = {https://pirsa.org/25090046},
            author = {Chen, Jing-Yuan},
            keywords = {Quantum Matter},
            language = {en},
            title = {Instanton and Chern-Simons in Lattice Yang-Mills Theory from Higher Category Theory},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {sep},
            note = {PIRSA:25090046 see, \url{https://scivideos.org/index.php/pirsa/25090046}}
          }

Jing-Yuan Chen Tsinghua IAS

Talk numberPIRSA:25090046
Source RepositoryPIRSA
Collection
Talk Type Other
Subject

Abstract

Putting continuum QFT (not just TQFT) onto the lattice is important for both fundamental understandings and numerical practices. The traditional way to do so, based on simple intuitions, however, does not admit natural definitions for general topological configurations of continuous-valued fields---the most prominent example being the lack of natural definition for Yang-Mills instanton in the practice of lattice QCD.
 
In this talk, I will develop a more systematic way to relate continuum QFT and lattice QFT, based on higher categories and higher anafunctors, so that the topological operators in the continuum can be naturally defined on the lattice. The idea, though formulated formally, is physically very intuitive---we want to effectively capture the different possibilities of how a lattice field may interpolate into the continuum. Therefore, the higher categorical concepts developed in higher homotopy theory are naturally involved. Via this formalism, we solve the long-standing problem of defining instanton and Chern-Simons term in lattice Yang-Mills theory using (a variant of) multiplicative bundle gerbe.
 
Notably, when the continuous-valued fields in our formalism become discrete-valued, our construction can recover the Dijkgraaf-Witten and Turaev-Viro theory, so we hope this formalism to be a good starting point towards (in the very long term) a more comprehensive categorical understanding of QFT that can encompass both continuous and discrete degrees of freedom, applicable both to IR and to UV.