TY - JOUR

T1 - Quantum phase transition and resurgence

T2 - Lessons from three-dimensional N = 4 supersymmetric quantum electrodynamics

AU - Fujimori, Toshiaki

AU - Honda, Masazumi

AU - Kamata, Syo

AU - Misumi, Tatsuhiro

AU - Sakai, Norisuke

AU - Yoda, Takuya

N1 - Funding Information:
The authors would like to thank Okuto Morikawa, Naohisa Sueishi, Hiromasa Takaura, and Yuya Tanizaki for valuable discussions. Preliminary results of this work have been presented in the KEK workshop "Thermal Quantum Field Theory and its Application" (August 2020), the YITP workshop YITP-W-20-08 "Progress in Particle Physics 2020" (September 2020), JPS meetings (September 2020 and March 2021), the YITP-RIKEN iTHEMS workshop YITP-T-20-03 "Potential Toolkit to Attack Nonperturbative Aspects of QFT: Resurgence and related topics" (September 2020), the 15th Kavli Asian Winter School on Strings, Particles and Cosmology (January 2021), and the Osaka City University Workshop "Randomness, Integrability and Representation Theory in Quantum Field Theory 2021" (March 2021). Discussions during the workshops were helpful in completing this work. M. H. is partially supported by MEXT Q-LEAP. This work is supported in part by Grant-in-Aid for Scientific Research (KAKENHI) (B) Grant Number 18H01217 (T. F., T. M., and N. S.). S. K. is supported by the Polish National Science Centre grant 2018/29/B/ST2/02457.
Publisher Copyright:
© 2021 The Author(s). Published by Oxford University Press on behalf of the Physical Society of Japan.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - 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 N = 4 supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has recently been 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 an anti-Stokes phenomenon occur 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 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.

AB - 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 N = 4 supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has recently been 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 an anti-Stokes phenomenon occur 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 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.

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U2 - 10.1093/ptep/ptab086

DO - 10.1093/ptep/ptab086

M3 - Review article

AN - SCOPUS:85119071796

SN - 2050-3911

VL - 2021

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

IS - 10

ER -