Color-Flavor Transformation for the Special Unitary Group

Abstract

We extend Zirnbauer's color-flavor transformation in the fermionic sector to the case of the special unitary group. The transformation allows a certain integral over SU(N_c) color matrices to be transformed into an integral over flavor matrices which parameterize the coset space U(2N_f)/U(N_f)xU(N_f). Integrals of the type considered appear, for example, in the partition function of lattice gauge theory.

Comments: 19 pages, 2 figures; typos fixed, normalization corrected, some arguments improved, appendix with special cases added; version to appear in Nucl. Phys. B