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Updated: Mar 22, 2026

Setting Limits on Supersymmetry Using Simplified Models
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Complex Path Integrals and Saddles in Two-Dimensional Gauge Theory.

P V Buividovich1, Gerald V Dunne2, S N Valgushev1,3

  • 1Institute for Theoretical Physics, Regensburg University, D-93053 Regensburg, Germany.

Physical Review Letters
|April 16, 2016
PubMed
Summary

This study numerically investigates saddle points in two-dimensional lattice gauge theory. Complex saddle points reveal new insights into nonperturbative effects and drive the phase transition through saddle condensation.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Computational Physics

Background:

  • Two-dimensional lattice gauge theories are fundamental models in quantum field theory.
  • Understanding nonperturbative effects is crucial for describing phenomena like phase transitions.
  • The Gross-Witten-Wadia model serves as a key example for studying these theories.

Purpose of the Study:

  • To numerically explore the complex saddle point structure of the two-dimensional lattice gauge theory.
  • To investigate the nature of nonperturbative effects in both weak and strong coupling phases.
  • To elucidate the mechanism driving the phase transition in this model.

Main Methods:

  • Numerical analysis of saddle points in the Gross-Witten-Wadia unitary matrix model.
  • Examination of complex-valued saddle points beyond the real integration variables.
  • Confirmation of established structures and identification of new interpretations.

Main Results:

  • Saddle points are generally complex-valued, deviating from real integration variables and action.
  • Trans-series and instanton gas structures are confirmed in the weak-coupling phase.
  • A novel complex-saddle interpretation for nonperturbative effects in the strong-coupling phase is identified.
  • Eigenvalue tunneling into the complex plane is observed in both phases.
  • Saddle condensation is identified as the driving mechanism for the weak-to-strong coupling phase transition.

Conclusions:

  • The study reveals the critical role of complex saddle points in understanding lattice gauge theories.
  • Nonperturbative effects and phase transitions are intricately linked to eigenvalue dynamics in the complex plane.
  • The findings offer a new perspective on the mathematical structure underlying these physical phenomena.