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WS22/23 – Abstract
Tin Sulejmanpasic
(Durham University)
14.12.2022
Lattice Villain Hamiltonians (PRETALK for students at 15:30 h)
Abelian gauge theories on the lattice often have less symmetries than their continuum counterparts. Namely a magnetic symmetry is violated by the presence of dynamical monopoles, which were believed to be an inevitable curse of lattice formulation. The magnetic symmetry has a mixed anomaly with an electric center symmetry, and hence the problem is reminiscent to the problem of chiral fermions on the lattice. A similar problem appears in compact scalar theories, where the presence of dynamical vortices ruins a corresponding U(1) symmetry. I will discuss the construction of Villain Hamiltonians for a compact scalar and U(1) gauge fields in various dimensions. Such models enjoy exact dualities, and allow for exactly self-dual formulation of electromagnetism. I will briefly discuss the possibility of a UV completion of such theories via interacting conformal fixed points.
