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

TL;DR

This paper extends the color-flavor transformation to SU(N) and uses it to analyze a 1+1 dimensional lattice QCD toy model, exploring baryon configurations and estimating their masses.

Contribution

It introduces an SU(N) extension of the color-flavor transformation and applies it to study baryons in a simplified lattice QCD model.

Findings

Identification of saddle-point configurations with different topological charges.

Estimation of baryon masses using saddle-point approximation for large N_c.

Analysis of static baryon definitions on the lattice.

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.