Color-Flavor Transformation for the Special Unitary Group
B. Schlittgen, T. Wettig
TL;DR
This paper extends Zirnbauer's color-flavor transformation to the special unitary group, enabling the conversion of integrals over SU(N_c) matrices into integrals over flavor matrices, with applications in lattice gauge theory.
Contribution
The paper introduces a novel extension of the color-flavor transformation specifically for the SU(N_c) group, broadening its applicability in theoretical physics.
Findings
Transformation applies to SU(N_c) matrices
Integral over color matrices becomes integral over flavor matrices
Facilitates calculations in lattice gauge theory
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.
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