PoS - Proceedings of Science
Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Theoretical Developments
A new type of lattice gauge theory through self-adjoint extensions
A. Mariani*, D. Banerjee, A. Banerjee, G. Kanwar, T. Rindlisbacher and U.J. Wiese
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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 $\theta$, 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 shows evidence of a broken $\mathbb{Z}_2$ symmetry in the continuum limit, in contrast to the ordinary theory.
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