Abelian scalar theory at large global charge

• Published in: Fortschritte der Physik Vol. 65; no. 9
• Main Author: Loukas, Orestis
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.09.2017
• Subjects: Computation; Couplings; Derivatives; Effective actions in perturbation theory; Goldstone's theorem; Ground state; Helium; High energy physics ‐ theory; Integrals; Quantum field theory
• ISSN: 0015-8208; 1521-3978
• DOI: 10.1002/prop.201700028

We elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and 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. The authors elaborate on Abelian complex scalar models, which are dictated by natural actions (all couplings are of order one), at fixed and large global U(1) charge in an arbitrary number of dimensions. The ground state is coherently constructed by the zero modes and the appearance of a centrifugal potential is quantum mechanically verified. Using the path integral formulation the quantum fluctuations around the ground state are sytematically analyzed in order to derive an effective action for the Goldstone mode. In this regime it is explicitly shown, 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.