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(N_c). Because the flavor group U(N_b, N_b) is non-compact, the algebraic method by which the original color-flavor transformation was derived leads to a useful result only for 2N_b \le N_c. Using the character expansion method, we obtain a different form of the transformation in the extended range N_b \le N_c. This result can also be used for the color group U(N_c). The integrals to which the transformation can be applied are of relevance for the recently proposed boson-induced lattice gauge theory.