1+1 Large $N_c$ QCD and its Holographic Dual -Soliton Picture of Baryons in Single-Flavor World

We study baryons in holographic QCD corresponding to 1+1 dimensional single-flavor ($N_f$=1) QCD for the first time. We formulate 1+1 QCD using an $S^1$-compactified D2/D8/$\overline{\rm D8}$ branes in the superstring theory, and describe the baryon as a topological configuration in 1+1 $N_f$=1 QCD, corresponding to $\Pi_1({\rm U(1)})={\bf Z}$. Unlike 1+3 QCD with $N_f \ge 2$, however, we find that the low-dimensional baryonic soliton is generally unstable against a scale transformation/variation and swells infinitely in 1+1 $N_f$=1 QCD at the leading of large $N_c$. We thus point out a serious difficulty on the soliton picture of baryons in large $N_c$ in the single-flavor world in both 1+1 and 1+3 QCD. We also compare the low-dimensional holographic baryon with the Abrikosov vortex, i.e., a stable topological configuration in Type-II superconductors.
Comment: 5 pages, 3 figures