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Howe Duality for an Induced Model of Lattice U(N) Yang-Mills Theory

J. Budczies·M. R. Zirnbauer
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Abstract

We propose an approach that views U(N_c) Yang-Mills theory as the critical point of an induced gauge model on the lattice. Similar recent proposals based on the color-flavor transformation rely on taking the limit of an infinite number of infinitely heavy particles. In contrast, we couple a finite number N_b of auxiliary boson flavors to the gauge field and argue that Yang-Mills theory is induced when N_b exceeds N_c and the boson mass is lowered to a critical point. Using the notion of Howe duality we transform the induced gauge model to a dual formulation in terms of local gauge invariant variables. In the abelian case the Howe duality transform turns out to coincide with the standard one, taking weakly coupled U(1)_{d=4} to strongly coupled Z_{d=4} lattice gauge theory.

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J. Budczies, M. R. Zirnbauer. 2003-08-15. Howe Duality for an Induced Model of Lattice U(N) Yang-Mills Theory. https://arxiv.org/abs/math-ph/0305058

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