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We developed a new Feynman integral method for conformal field theory calculations. This approach simplifies complex calculations for scalar n-point functions and reveals insights into anomalies and beta functions.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory

Background:

  • Conformal field theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
  • Calculating n-point functions in momentum space is essential for CFT analysis.

Purpose of the Study:

  • To introduce a general Feynman integral representation for scalar n-point functions in CFTs.
  • To solve conformal Ward identities and identify momentum-space conformal cross ratios.

Main Methods:

  • Developed a Feynman integral representation for general scalar n-point functions.
  • The representation involves integrations over momenta on an (n-1) simplex.
  • Analyzed the simplest nontrivial case: 4-point functions.

Main Results:

  • The representation depends on an arbitrary function of n(n-3)/2 variables (conformal cross ratios).
  • Identified conditions for singularities, anomalies, and beta functions in 4-point functions.
  • Demonstrated applications in perturbative quantum field theory and holography.

Conclusions:

  • The new representation offers a powerful tool for CFT research.
  • It provides a systematic way to study anomalies and beta functions.
  • The method is applicable to various areas of quantum field theory and related fields.