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We introduce a novel analytical method for conformal field theories (CFTs) using bootstrap and Mellin representations. This approach reproduces known results and yields new, higher-order predictions for critical phenomena like the 3D Ising model.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory

Background:

  • Conformal Field Theories (CFTs) describe critical phenomena and systems with scale invariance.
  • Analytical solutions for CFTs are challenging, often relying on approximations or numerical methods.

Purpose of the Study:

  • To develop a new analytical technique for solving CFTs.
  • To leverage the bootstrap philosophy and Mellin representation for CFT amplitude analysis.

Main Methods:

  • Utilizing exchange Witten diagrams with built-in crossing symmetry.
  • Applying the Mellin representation to CFT amplitudes.
  • Imposing operator product expansion (OPE) consistency for constraints.

Main Results:

  • Successfully reproduced anomalous dimensions in the epsilon (ε) expansion of the Wilson-Fisher fixed point.
  • Obtained operator product expansion (OPE) coefficients to higher orders in ε than previously possible analytically.
  • Achieved improved agreement between theoretical predictions and numerical results for the 3D Ising model.

Conclusions:

  • The proposed method offers a powerful new tool for analytical CFT calculations.
  • This approach advances the understanding of critical phenomena and provides more accurate predictions.
  • It opens avenues for exploring complex CFTs and their applications.