7–9 Dec 2022
Online (Zoom)
Asia/Tokyo timezone

Fractional topological charge in lattice Abelian gauge theory

7 Dec 2022, 15:00
20m
Online (Zoom)

Online (Zoom)

The necessary information (links, IDs, and passcodes) will be sent to the participants by E-mail before the workshop starts.

Speaker

Mr Motokazu Abe (Kyushu University)

Description

Since Gaiotto et.~al discussed the low-energy dynamics of gauge theories on the basis of the mixed ’t Hooft anomaly between discrete and higher-form symmetries, this type of application of the anomaly has been studied vigorously. In this study, in order to understand this type of application of the anomaly in a completely regularized framework, we formulate the fractional topological charge associated with the U(1)/Zq principal bundle in the compact U(1) lattice gauge theory by generalizing L\“uscher’s construction. This fractional topological charge in lattice gauge theory is Zq one-form gauge invariant and odd under the lattice time reversal transformation. By employing these properties of the fractional topological charge, we can show that the U(1) gauge theory containing matter fields with charge q2Z has the mixed ’t Hooft anomaly between the Zq one-form symmetry and the time reversal symmetry when θ=π. This is analogous to the mixed ’t Hooft anomaly between the ZN one-form symmetry and the time reversal symmetry in SU(N)/ZN theory when θ=π.

Primary author

Mr Motokazu Abe (Kyushu University)

Presentation materials