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

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.

23+16 pages, 14 figures

References in corpus (35)

• Notes on SUSY Gauge Theories on Three-Sphere
• Open string amplitudes and large order behavior in topological string theory
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Structure of Lefschetz thimbles in simple fermionic systems
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling
• Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$ SYM
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Deconstructing zero: resurgence, supersymmetry and complex saddles
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Resumming the string perturbation series
• Monte Carlo calculations of the finite density Thirring model
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Introduction to 1-summability and resurgence
• Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Uniformization and Constructive Analytic Continuation of Taylor Series
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Finite N from Resurgent Large N
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• A new method to sum divergent power series: educated match
• Resurgence of the large-charge expansion
• Resurgence in the O(4) sigma model
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• From perturbative to non-perturbative in the O(4) sigma model
• On Perturbation theory improved by Strong coupling expansion
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Quantum phase transition in many-flavor supersymmetric QED${}_3$
• Resurgence in the Bi-Yang-Baxter Model
• Resurgent Analysis of Ward-Schwinger-Dyson Equations
• Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres $\Sigma (2,3,6n+5)$
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• More on the infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$

Cited by in corpus (7)

• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Resurgence and self-completion in renormalized gauge theories
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD
• The QCD Adler function and the muon $g-2$ anomaly from renormalons
• Complex Saddles of Charged-AdS Gravitational partition function
• Exact WKB in all sectors II: Potentials with non-degenerate saddles