Abelian scalar theory at large global charge

TL;DR

This paper studies Abelian complex scalar models at large fixed global charge, deriving an effective Goldstone action and demonstrating stability against quantum corrections in arbitrary dimensions.

Contribution

It provides a systematic analysis of quantum fluctuations and effective actions for large-charge Abelian scalar theories, confirming their stability and suppression of higher derivative terms.

Findings

Effective Goldstone action derived at large charge

Quantum fluctuations are systematically analyzed

Higher derivative couplings are suppressed at large charge

Abstract

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 $| \upsilon\rangle$ 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 $| \upsilon\rangle$ 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 that the whole construction is stable against quantum corrections, in the sense that any higher derivative couplings to Goldstone's tree-level action are suppressed by appropriate powers of the large charge.