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

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

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

Aug 8, 2022, 4:50 PM
20m
CP1-HSZ/1st-1.001 - HS5 (CP1-HSZ)

### CP1-HSZ/1st-1.001 - HS5

#### CP1-HSZ

50
Oral Presentation Theoretical Developments and Applications beyond Particle Physics

### 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.

### Primary authors

Alessandro Mariani (University of Bern) Gurtej Kanwar (University of Bern) Tobias Rindlisbacher (AEC, Institute for Theoretical Physics, University of Bern) Uwe-Jens Wiese (University of Bern, Switzerland) Prof. Debasish Banerjee (Saha Institute of Nuclear Physics) Dr Aditya Banerjee (Saha Institute of Nuclear Physics)