Bosonic color-flavor transformation for the special unitary group
Abstract
We extend Zirnbauer's color-flavor transformation in the bosonic sector to the color group SU(Nc). Because the flavor group U(Nb, Nb) is non-compact, the algebraic method by which the original color-flavor transformation was derived leads to a useful result only for 2Nb Nc. Using the character expansion method, we obtain a different form of the transformation in the extended range Nb Nc. This result can also be used for the color group U(Nc). The integrals to which the transformation can be applied are of relevance for the recently proposed boson-induced lattice gauge theory.
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