清华大学高等研究院

摘要：

Putting U(1) Chern-Simons onto the lattice has been a problem of interest for decades. Over time, there has been many scattered ideas, and we identify two as being crucial: First, to correctly capture the topology of U(1), the U(1) lattice gauge field must be in the Villainized form (Villainization is one key idea behind the discovery of BKT transition). Second, a crucial feature of the theory is that it is chiral, so that the theory cannot be fully topological, some non-topological terms such as a Maxwell term is needed. Putting these two ideas together, we defined and solved the U(1) Chern-Simons-Maxwell theory on the lattice, obtaining all the key features---including, most non-trivially, the chiral gravitational/framing anomaly. We consider this as completion of the problem of defining chiral U(1) Chern-Simons on the lattice.

There is another long standing problem, in the field of lattice QCD:  To find a natural definition for Yang-Mills instanton on the lattice (and this is also related to the problem of defining non-abelian Chern-Simons on lattice). We need to generalize the Villaination of U(1) lattice gauge field to SU(N), and it turns out this is highly non-trivial---the generalization must be achieved through the lens of higher category theory. More broadly, the categorical perspective leads to a more systematic picture of how continuum QFT and lattice QFT are related.

报告人简介：

Jing-Yuan Chen is a faculty at the Institute for Advanced Study at Tsinghua University. He received B.Sc. in physics and pure mathematics at the University of Michigan Ann Arbor in 2011, and Ph.D. in physics, supervised by Dam Thanh Son, at the University of Chicago in 2016. After that he worked as a Gordon and Betty Moore Postdoctoral Fellow at Stanford Institute for Theoretical Physics, until joining the current position in 2020.

主持人：周毅

地点：M楼837