Abelian scalar theory at large global charge

Loukas, Orestis (2017). Abelian scalar theory at large global charge. Fortschritte der Physik / Progress of physics, 65(9), p. 1700028. Wiley-VCH 10.1002/prop.201700028

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We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixedand large global U(1) charge in an arbitrary number of dimensions. The ground state |v〉is coherently constructed by the zero modes and the appearance of a centrifugal potential is quantum mechanically verified. Using the path integral formulation we systematically analyze the quantum fluctuations around |v〉in order to derive an effective action for the Goldstone mode, which becomes perturbatively meaningful when the charge is large. In this regime we explicitly show, by computing the first few loop corrections, that the whole construction is stable against quantum effects, in the sense that any higher derivative couplings to Goldstone’s tree-level action are suppressed by appropriate powers of the large charge.

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