Quantum Hall liquids in high-density QCD

Abstract

There exist metastable domain walls of the flavor-singlet meson $\hat{I}\cdot$ for the $\mathrm{U}(1)$ axial symmetry in two-flavor color superconductivity (2SC) in QCD at large baryon density. We show that, due to the coupling of $\hat{I}\cdot$ to confined $\mathrm{SU}(2)$ gluons in the 2SC phase, the effective theory on the domain wall is described by the $\mathrm{SU}(2{)}_{-1}$ Chern-Simons theory, which is dual to the $\mathrm{U}(1{)}_2$ Chern-Simons theory. This theory has a spin-1 droplet excitation that does not carry a baryon number, which we identify as a vector meson. We also discuss the effective theories and baryonic droplet excitations on the domain walls of the flavor-singlet mesons in the superfluid phases of QCD at large isospin density and two-color QCD at large baryon density.

13 pages; v2: minor revisions, published version