Abstract
We study reflection and transmission of light at the interface between different phases of a $U(1)\ensuremath{\bigotimes}U(1)$ gauge theory. On each side of the interface, one can choose a basis so that one generator is free (allowing propagation of light), and the orthogonal one may be free, have a Higgs phase, or be confined. However, the basis on one side will in general be rotated relative to the basis on the other by some angle $\ensuremath{\alpha}.$ We calculate reflection and transmission coefficients for both polarizations of light and all 8 types of boundary, for arbitrary $\ensuremath{\alpha}.$ We find that an observer measuring the behavior of light beams at the boundary would be able to distinguish 4 different types of boundary, and we show how the remaining ambiguity arises from the principle of complementarity (indistinguishability of confined and Higgs phases) which leaves observables invariant under a global electric/magnetic duality transformation. We also explain the seemingly paradoxical behavior of Higgs/Higgs and confined/confined boundaries, and clarify some previous arguments that confinement must involve magnetic monopole condensation.
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