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arXiv · 1705.05825

A Note on Inhomogeneous Ground States at Large Global Charge

Simeon Hellerman·Nozomu Kobayashi·Shunsuke Maeda·Masataka Watanabe
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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 $ρ_{1,2}$. 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 $ρ_1 / ρ_2$. 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 $ρ_1 / ρ_2$ 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.

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Simeon Hellerman, Nozomu Kobayashi, Shunsuke Maeda, Masataka Watanabe. 2017-05-16. A Note on Inhomogeneous Ground States at Large Global Charge. https://doi.org/10.1007/jhep10(2019)038

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