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

Solitonic symmetry beyond homotopy: invertibility from bordism and non-invertibility from TQFT

7 Dec 2022, 14:20
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 Shi Chen (The University of Tokyo)

Description

Solitonic symmetry is believed to follow the homotopy-group classification of topological solitons. Here, we point out a more sophisticated algebraic structure when solitons of different codimensions coexist in the spectrum. We uncover this phenomenon in a concrete quantum field theory, the 4d CP1 model. This model has two kinds of solitonic excitations, vortices and hopfions, which would follow two U(1) solitonic symmetries according to homotopy groups. Nevertheless, we demonstrate the nonexistence of the hopfion U(1) symmetry by evaluating the hopfion charge of vortex operators. We clarify that what conserves hopfion numbers is a non-invertible symmetry generated by 3d spin topological quantum field theories (TQFTs). Its invertible subgroup is just Z2, which we recognize as a spin bordism invariant. Compared with the 3d CP1 model, our work suggests a unified description of solitonic symmetries and couplings to topological phases.

Primary author

Mr Shi Chen (The University of Tokyo)

Presentation materials