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We explore multicritical universality classes in coupled vector-field models using the functional renormalization group and the epsilon-expansion. A new fixed point was discovered, and complete renormalization group trajectories were established for asymptotically safe and infrared-complete theories.

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Area of Science:

  • Quantum Field Theory
  • Statistical Mechanics
  • High-Energy Physics

Background:

  • Understanding multicritical phenomena is crucial for various areas of physics.
  • Coupled vector-field models serve as important testbeds for theoretical frameworks.
  • Exploring theories that are both asymptotically safe and infrared complete is a key goal in modern physics.

Purpose of the Study:

  • To investigate multicritical universality classes in coupled vector-field models in three dimensions.
  • To utilize the complementary strengths of the functional renormalization group and the epsilon-expansion.
  • To explore these models as toy systems for theories with desirable ultraviolet and infrared properties.

Main Methods:

  • Concerted application of the functional renormalization group and the epsilon-expansion.
  • Analysis of three- and four-field models with numerous interactions and symmetry-breaking patterns.
  • Investigation of renormalization group trajectories.

Main Results:

  • Discovery of a new fixed point arising from inter-field sector interactions.
  • Establishment of the absence of infrared-stable fixed-point solutions for small epsilon.
  • Demonstration of complete renormalization group trajectories starting and ending at nontrivial fixed points.

Conclusions:

  • The combined methods provide a powerful approach for studying complex field theories.
  • These models serve as valuable toy examples for theories exhibiting asymptotic safety and infrared completeness.
  • The findings contribute to the understanding of critical phenomena and the behavior of quantum field theories.