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Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
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Homoclinic Renormalization Group Flows, or When Relevant Operators Become Irrelevant.

Christian B Jepsen1, Fedor K Popov2

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This study explores a supersymmetric quantum field theory, revealing novel bifurcations in renormalization group flow. Researchers found evidence of homoclinic RG flow, a unique behavior where the flow returns to its starting point.

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Area of Science:

  • Quantum Field Theory
  • High Energy Physics
  • Mathematical Physics

Background:

  • N=1 supersymmetric quantum field theory with O(M)×O(N) symmetry.
  • Renormalization group (RG) flow analysis is crucial for understanding quantum field theories.

Purpose of the Study:

  • Investigate the RG flow and fixed points of an N=1 supersymmetric quantum field theory in 3-ε dimensions.
  • Analyze the impact of O(M)×O(N) symmetry and general real values for N and M as bifurcation parameters.
  • Identify and characterize novel bifurcations and fixed points, including logarithmic conformal field theories.

Main Methods:

  • Calculation of beta functions up to second loop order.
  • Detailed analysis of renormalization group flow and fixed points in the space of M and N.
  • Demarcation of regions with nonmonotonic RG flow and identification of Hopf bifurcation curves.
  • Investigation of Bogdanov-Takens bifurcations and associated fixed points with non-diagonalizable stability matrices.

Main Results:

  • Identified regions of nonmonotonic RG flow and curves of Hopf bifurcations.
  • Discovered fixed points with non-diagonalizable stability matrices and Jordan blocks of size two with zero eigenvalues.
  • Demonstrated the existence of logarithmic conformal field theories and Bogdanov-Takens bifurcations.
  • Provided analytic and numeric evidence for the existence of homoclinic RG flow.

Conclusions:

  • The studied supersymmetric quantum field theory exhibits complex RG flow behavior, including bifurcations and fixed points characteristic of logarithmic conformal field theories.
  • Homoclinic RG flows, originating and terminating at the same fixed point, were analytically and numerically confirmed.
  • The findings contribute to a deeper understanding of phase transitions and critical phenomena in quantum field theories.