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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
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Resurgence of TT[over ¯]-Deformed Partition Function.

Jie Gu1, Yunfeng Jiang1,2, Huajia Wang2,3

  • 1Southeast University, School of Physics and Shing-Tung Yau Center, Nanjing 211189, People's Republic of China.

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This study investigates nonperturbative effects in 2D conformal field theory (CFT) using resurgence. We found that the deformed partition function

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • The TT[over ¯]-deformation introduces nonperturbative effects into 2D conformal field theories (CFTs).
  • Understanding these effects is crucial for a complete description of quantum field theories.

Purpose of the Study:

  • To study the nonperturbative effects of the torus partition function in TT[over ¯]-deformed 2D CFTs.
  • To develop efficient methods for computing perturbative coefficients and analyze their asymptotic behavior.

Main Methods:

  • Development of efficient algorithms for calculating high-order perturbative coefficients in the deformation parameter λ.
  • Application of resurgence techniques to extract nonperturbative contributions from perturbative data.
  • Analytical continuation of modular parameters in the partition function's integral representation.

Main Results:

  • Computation of the first 600 perturbative coefficients for TT[over ¯]-deformed free boson and free fermion.
  • Numerical evidence demonstrating the asymptotic and non-Borel resummmable nature of the λ series.
  • Identification of new complex saddle points as the origin of nonperturbative effects.

Conclusions:

  • The study provides strong evidence for nonperturbative effects arising from complex saddle points in deformed CFTs.
  • The findings offer insights into the Stokes phenomenon and potential connections to holographic dualities.
  • The developed methods are generalizable to other rational CFTs.