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The Anderson transition between localized and metallic states istraditionally analyzed by assuming a one-parameter scaling hypothesis. Althoughthat hypothesis has been confirmed near two dimensions by epsilon = d-2expansion of the Wegner-Efetov nonlinear sigma model, there exists mountingevidence that the transition in d=3 or higher may have a second branch and thattwo relevant parameters are needed in order to describe the universal behaviorat criticality. Doubt of the standard hypothesis also comes from field theory.Indeed, increasing the space dimension pushes the Anderson transition towardsstrong disorder, where a strong-coupling approach very different from the usualweak-coupling analysis of the sigma model is called for. In the present work,we develop a novel field theory of Anderson transitions at strong couplingbased on the key observation that the U(1) symmetry which distinguishesretarded from advanced fields may undergo spontaneous symmetry breaking. Thatsymmetry breakdown splits the sigma model coupling into two, thus leading to anatural scenario of two-parameter scaling. While we develop the field theoryfrom the concrete starting point of the Wegner N-orbital model, we believe ourresults to be of much wider applicability. The first of a series, the presentpaper offers a pedagogical introduction to the main ideas in the setting of theone-replica theory. Subsequent papers will employ the self-consistentapproximation of Abou-Chacra et al. and develop the full supersymmetric theory.The latter establishes the existence of a new renormalization-group fixedpoint, whose basin of attraction constitutes a third phase of disorderedelectronic matter.

Wegner model in high dimension: U(1) symmetry breaking and a non-standard phase of disordered electronic matter, I. One-replica theory