A Note on Inhomogeneous Ground States at Large Global Charge

Abstract

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. This suggests that the scale of variation of the ground state solution in finite volume will be the infrared scale, and that the use of the effective theory at large charge in finite volume is self-consistent.

13 pages, LaTeX

References in corpus (4)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Conformal dimensions in the large charge sectors at the O(4) Wilson-Fisher fixed point
• Abelian scalar theory at large global charge

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