U(1) lattice gauge theory with a topological action

We investigate the phase diagram of the compact $U(1)$ lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous deformations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. The topological action offers an algorithmic advantage for the computation of the free energy.We investigate the phase diagram of the compact U(1) lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous de-formations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. However, since the monopoles do not influence the long-distance prop-erties of the Coulomb phase, the physics is smooth across the singularity in the monopole density. The topological action offers an algorithmic advantage for the computation of the free energy.We investigate the phase diagram of the compact $U(1)$ lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous deformations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. The topological action offers an algorithmic advantage for the computation of the free energy