The 39th International Symposium on Lattice Field Theory (Lattice 2022)

A new type of lattice gauge theory through self-adjoint extensions

8 Aug 2022, 16:50

20m

CP1-HSZ/1.001 (CP1-HSZ) - HS5 (CP1-HSZ)

Oral Presentation Theoretical Developments and Applications beyond Particle Physics Theoretical Developments

Speaker

Alessandro Mariani (University of Bern)

Description

A generalization of Wilsonian lattice gauge theory may be obtained by considering the possible self-adjoint extensions of the electric field operator in the Hamiltonian formalism. In the special case of $3D$ $U(1)$ gauge theory these are parametrised by a phase $\theta$, and the ordinary Wilson theory is recovered for $\theta =0$. We consider the case $\theta =\pi$, which, upon dualization, turns into a theory of staggered integer and half-integer height variables. We investigate order parameters for the breaking of the relevant symmetries, and thus study the phase diagram of the theory, which could reveal a new universality class of $3D$ Abelian gauge theories with a broken ${\mathbb{Z}}_2$ symmetry absent in the ordinary theory.

Presentation materials

New type of lattice gauge theory.pdf