Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED

TL;DR

This paper explores the connection between resurgence theory and quantum phase transitions in 3d $ abla=4$ SQED, revealing how phase transition phenomena are reflected in the structure of Lefschetz thimbles and Borel plane singularities.

Contribution

It provides a detailed analysis of the resurgence structure in 3d $ abla=4$ SQED and interprets the phase transition through Lefschetz thimbles and Borel resummation, linking resurgence to phase transition behavior.

Findings

Second-order phase transition characterized by saddle collisions.

Simultaneous Stokes and anti-Stokes phenomena at the critical point.

Infinite Stokes phenomena due to supersymmetry, mapped to Borel plane structures.

Abstract

We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has been recently proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and anti-Stokes phenomenon occurs simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from the SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique.