Large charge bootstrap with U(1) current probes

TL;DR

This work extends the large-charge conformal bootstrap to CFTs with a global $U(1)$ current by incorporating vector probes, revealing new bootstrap constraints absent in the scalar-only case. Under the assumptions of a finite number of Regge trajectories and a nontrivial macroscopic limit, the authors show that current probes impose $Q_N(0)=0$, aligning bootstrap data with Goldstone EFT expectations. They analyze one- and two-Regge-trajectory solutions, demonstrating that the two-trajectory sector can be realized by local EFTs with additional light fields (scalar, vector, or rank-2 tensor), thereby strengthening the bootstrap-EFT connection in large-charge sectors. The results suggest a tighter framework for matching bootstrap data to EFTs and motivate further exploration with higher-spin probes and unitarity constraints to sharpen the landscape of admissible theories.

Abstract

We study the large-charge bootstrap for conformal field theories with a U(1) symmetry extending the analysis of scalar probes to include conserved currents. We formulate the bootstrap equations and analyze their solutions assuming the existence of a non-trivial macroscopic limit and that the spectrum organizes into a finite number of Regge trajectories. We show that current probes lead to additional bootstrap constraints that are absent in the purely scalar case, and we classify the resulting solutions.