A New Type of Lattice Gauge Theory through Self-adjoint Extensions

Abstract

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 $\mathrm{U}(1)$ gauge theory these are parametrised by a phase $\hat{I}¸$, and the ordinary Wilson theory is recovered for $\hat{I}¸=0$. We consider the case $\hat{I}¸=\ddot{I}€$, 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 shows evidence of a broken ${\mathbb{Z}}_2$ symmetry in the continuum limit, in contrast to the ordinary theory.

Proceedings for the 39th International Symposium on Lattice Field Theory, LATTICE2022