KEK Theory Workshop 2022

Boson-fermion duality with subsystem symmetry

7 Dec 2022, 15:20

20m

Online (Zoom)

Parallel session A

Speaker

Mr Weiguang Cao (Kavli IPMU, University of Tokyo)

Description

In this talk, I will introduce an exact duality in (2 + 1)d between the fermionization of a bosonic theory with a $Z_2$ subsystem symmetry and a fermionic theory with a $Z_2$ subsystem fermion parity symmetry. A typical example is the duality between the fermionization of the plaquette Ising model and the plaquette fermion model. I will establish the exact duality on the lattice by using the generalized Jordan-Wigner map, with a careful discussion on the mapping of the twist and symmetry sectors. This motivates us to introduce the subsystem Arf invariant, which exhibits a foliation structure.