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We used the conformal bootstrap to find universal constraints on operator dimensions in 3D theories with N=2 supersymmetry. This method precisely determined the spectrum of the critical Wess-Zumino model, matching exact calculations.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Supersymmetry

Background:

  • Conformal field theories (CFTs) in 3D with N=2 supersymmetry are crucial for understanding critical phenomena.
  • The conformal bootstrap is a powerful, non-perturbative method for studying CFTs.

Purpose of the Study:

  • To apply the conformal bootstrap program to 3D CFTs with N=2 supersymmetry.
  • To derive universal constraints on operator dimensions and critical exponents.
  • To precisely determine the spectrum of the critical 3D N=2 Wess-Zumino model.

Main Methods:

  • Implementation of the conformal bootstrap program.
  • Analysis of operator product expansions (OPEs) of chiral and antichiral operators.
  • Identification of kinks in the allowed spectrum of operator dimensions.

Main Results:

  • Universal constraints on operator dimensions were found for 3D N=2 supersymmetric CFTs.
  • A kink was identified at the predicted location of the critical 3D N=2 Wess-Zumino model.
  • The low-lying operator dimension spectrum and stress-tensor two-point function were determined with high accuracy.

Conclusions:

  • The conformal bootstrap provides accurate predictions for critical 3D N=2 supersymmetric theories.
  • The results for the Wess-Zumino model show excellent agreement with exact computations, validating the bootstrap approach.