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We study reflection and transmission of light at the interface betweendifferent phases of a U(1) x U(1) gauge theory. On each side of the interface,one can choose a basis so that one generator is free (allowing propagation oflight), and the orthogonal one may be free, Higgsed, or confined. However, thebasis on one side will in general be rotated relative to the basis on the otherby some angle alpha. We calculate reflection and transmission coefficients forboth polarizations of light and all 8 types of boundary, for arbitrary alpha.We find that an observer measuring the behavior of light beams at the boundarywould be able to distinguish 4 different types of boundary, and we show how theremaining ambiguity arises from the principle of complementarity(indistinguishability of confined and Higgs phases) which leaves observablesinvariant under a global electric/magnetic duality transformation. We alsoexplain the seemingly paradoxical behavior of Higgs/Higgs and confined/confinedboundaries, and clarify some previous arguments that confinement must involvemagnetic monopole condensation.Comment: RevTeX, 12 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Illuminating interfaces between phases of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /><mml:mo>×</mml:mo><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>gauge theory

Illuminating interfaces between phases of aU(1)×U(1)gauge theory