Bosonic color-flavor transformation for the special unitary group

TL;DR

This paper extends the bosonic color-flavor transformation to the SU(N_c) group, providing new formulas applicable for a broader range of parameters, with implications for lattice gauge theories.

Contribution

It introduces a new form of the bosonic color-flavor transformation valid for N_b  N_c using character expansion, expanding the applicability beyond previous limitations.

Findings

Derived a new transformation form for N_b  N_c

Applicable to U(N_c) color group integrals

Relevance for boson-induced lattice gauge theory

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.