Real-time dynamics of Chern-Simons fluctuations near a critical point

TL;DR

This study investigates the real-time behavior of topological fluctuations in a 1+1 dimensional Schwinger model with a theta-term, revealing a sharp susceptibility peak near a critical point, with implications for QCD and ferroelectrics.

Contribution

It provides the first analysis of real-time topological susceptibility near a critical point in the Schwinger model, linking critical fluctuations to topological properties.

Findings

Sharp maximum in topological susceptibility at critical point

Growth of critical fluctuations interpreted from correlation functions

Analogies drawn with QCD and ferroelectric phase transitions

Abstract

The real-time topological susceptibility is studied in $(1+1)$-dimensional massive Schwinger model with a $\theta$-term. We evaluate the real-time correlation function of electric field that represents the topological Chern-Pontryagin number density in $(1+1)$ dimensions. Near the parity-breaking critical point located at $\theta=\pi$ and fermion mass $m$ to coupling $g$ ratio of $m/g \approx 0.33$, we observe a sharp maximum in the topological susceptibility. We interpret this maximum in terms of the growth of critical fluctuations near the critical point, and draw analogies between the massive Schwinger model, QCD near the critical point, and ferroelectrics near the Curie point.