Chern-Simons-Matter Theories at Large Baryon Number

Understand

We study $SU(2)$ Chern-Simons theories at level $k$ coupled to a scalar on $T^2\times \mathbb{R}$ at large baryon number.

• We find a homogeneous but anisotropic ground state configuration for any values of $k$ on the IR fixed-point of those models.
• This classical analysis is valid as long as we take the baryon number large.
• As a corollary, by comparing the symmetry breaking pattern at large chemical potential, we find that the theory does not reduce to the singlet sector of the $O(4)$ Wilson-Fisher fixed-point at large-$k$, as expected from general grounds.