A note on inhomogeneous ground states at large global charge

  • Simeon Hellerman
  • Nozomu Kobayashi
  • Shunsuke Maeda
  • Masataka WatanabeEmail author
Open Access
Regular Article - Theoretical Physics


In this note we search for the ground state of the D = 3 Wilson-Fisher conformal O(4) model, at nonzero values of the two independent charge densities ρ1,2, on the torus spatial slice. 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 ρ1/ρ2. This result confirms, within the context of a well-defined effective theory, a recent no-go result of [1]. We also show that any spatially periodic ground state solutions have an energetic preference towards longer periods, within some range of ρ1/ρ2 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. Note added: the statements in this paper are true for arbitrary ratio of ρ1/ρ2, which we proved after we uploaded this paper. See [2].


Conformal Field Theory Effective Field Theories Global Symmetries 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Kavli Institute for the Physics and Mathematics of the Universe (WPI)The University of Tokyo Institutes for Advanced Study, The University of TokyoKashiwaJapan
  2. 2.Department of Physics, Faculty of ScienceThe University of TokyoTokyoJapan

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