Yukawa interactions at Large Charge

TL;DR

This paper extends the fixed-charge semiclassical method to compute anomalous dimensions in models with Yukawa interactions, providing new predictions for both weakly and strongly coupled regimes, and connecting to future computational approaches.

Contribution

It introduces an extension of the fixed-charge semiclassical method to Yukawa-interacting models, including Nambu-Jona-Lasinio-Yukawa and gauge-Yukawa theories, with new predictions for anomalous dimensions.

Findings

Results match known perturbative orders in weak coupling.

Predictions for higher-order terms in perturbation theory.

Matching with large-charge effective field theory in strong coupling.

Abstract

We extend the fixed-charge semiclassical method by computing anomalous dimensions of fixed-charge scalar operators in models with Yukawa interactions. In particular, we discuss the Nambu-Jona-Lasinio-Yukawa theory as well as an asymptotically safe gauge-Yukawa model in four dimensions. In the weakly coupled regime, we cross-check our results to the respective maximum known orders of perturbation theory in these models and predict higher order terms for future comparisons with other computational methods. In the strongly coupled regime, we match our results to the predictions of the large-charge effective field theory which can be compared to future Monte Carlo and lattice studies.