A Note on Inhomogeneous Ground States at Large Global Charge

Understand

In this note we search for the ground state, in infinite volume, of the $D=3$ Wilson-Fisher conformal $O(4)$ model, at nonzero values of the two independent charge densities $\rho_{1,2}$.

• Using an effective theory valid on scales longer than the scale defined by the charge density, we show that the ground-state configuration is inhomogeneous for generic ratios $\rho_1 / \rho_2$.
• This result confirms, within the context of a well-defined effective theory, a recent no-go result of Alvarez-Gaume' et al.
• We also show that any spatially periodic ground state solutions have an energetic preference towards longer periods, within some range of $\rho_1 / \rho_2$ containing a neighborhood of zero.