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Critical Look at β-Function Singularities at Large N.

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We developed a self-consistency equation for beta functions in theories with many flavors (N). This method removes singularities, suggesting no UV fixed point exists in the large-N limit for gauge theories.

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Area of Science:

  • High Energy Physics
  • Quantum Field Theory
  • Statistical Mechanics

Background:

  • Understanding the behavior of quantum field theories, especially in the large-N limit, is crucial for theoretical physics.
  • Critical exponents, like the Wilson-Fisher critical exponent (ω), provide insights into phase transitions but can exhibit singularities.
  • Beta functions describe how coupling constants change with energy scale and are key to determining theory behavior.

Purpose of the Study:

  • To propose a novel self-consistency equation for beta functions in theories with a large number of flavors (N).
  • To investigate the relationship between singularities in critical exponents and the beta function.
  • To analyze the implications for the existence of UV fixed points in (non-)Abelian gauge theories.

Main Methods:

  • Developing a self-consistency equation for beta functions, incorporating information from the Wilson-Fisher critical exponent (ω).
  • Truncating the analysis at a fixed order in the 1/N expansion.
  • Applying the method to (non-)Abelian gauge theories to study the behavior of beta functions and fermion mass anomalous dimensions.

Main Results:

  • Demonstrating that singularities in critical exponents do not necessarily imply singularities in the beta function.
  • Observing that the critical exponent ω features a negative singularity in (non-)Abelian gauge theories.
  • Showing the simultaneous removal of singularities in the beta function and fermion mass anomalous dimension.

Conclusions:

  • The proposed self-consistency equation provides a consistent framework for analyzing beta functions in the large-N limit.
  • The simultaneous removal of singularities suggests the absence of a UV fixed point in the large-N limit for the studied gauge theories.
  • This work offers new insights into the non-perturbative behavior of quantum field theories.