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arXiv · hep-lat/0112018

(1+1)-dimensional Baryons from the SU(N) Color-Flavor Transformation

J. Budczies·S. Nonnenmacher·Ya. Shnir·M. R. Zirnbauer
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Abstract

The color-flavor transformation, an identity that connects two integrals, each of which is over one of a dual pair of Lie groups acting in the fermionic Fock space, is extended to the case of the special unitary group. Using this extension, a toy model of lattice QCD is studied: N_f species of spinless fermions interacting with strongly coupled SU(N_c) lattice gauge fields in 1+1 dimensions. The color-flavor transformed theory is expressed in terms of gauge singlets, the meson fields, organized into sectors distinguished by the distribution of baryonic flux. A comprehensive analytical and numerical search is made for saddle-point configurations of the meson fields, with various topological charges, in the vacuum and single-baryon sectors. Two definitions of the static baryon on the square lattice, straight and zigzag, are investigated. The masses of the baryonic states are estimated using the saddle-point approximation for large N_c.

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J. Budczies, S. Nonnenmacher, Ya. Shnir, M. R. Zirnbauer. 2001-12-14. (1+1)-dimensional Baryons from the SU(N) Color-Flavor Transformation. https://doi.org/10.1016/s0550-3213(02)00331-0

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