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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Renormalization group flows, cycles, and c-theorem folklore.

Thomas L Curtright1, Xiang Jin, Cosmas K Zachos

  • 1Department of Physics, University of Miami, Coral Gables, Florida 33124-8046, USA.

Physical Review Letters
|May 1, 2012
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Summary
This summary is machine-generated.

Monotonic renormalization group flows, typically preventing cyclic trajectories, may allow them if the flow function is multivalued. This challenges assumptions about coupling behaviors in quantum field theory.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Renormalization group methods

Background:

  • Renormalization group (RG) flows describe how physical parameters change with energy scale.
  • Monotonicity of RG flows for specific functions (like 'c' and 'a') is a key concept.
  • This monotonicity is widely believed to preclude cyclic or chaotic coupling trajectories.

Purpose of the Study:

  • To investigate the compatibility of monotonic RG flows with cyclic coupling trajectories.
  • To challenge the established understanding that monotonic flows prevent cyclic behaviors.
  • To explore conditions under which cyclic flows might coexist with monotonic functions.

Main Methods:

  • Analysis of simple, illustrative examples.
  • Theoretical examination of renormalization group flow equations.
  • Investigation of the properties of multivalued functions in the context of couplings.

Main Results:

  • Demonstration that monotonic RG flows do not universally prohibit cyclic coupling trajectories.
  • Identification of multivalued flow functions as a mechanism allowing simultaneous monotonic and cyclic behaviors.
  • Simple examples illustrating the coexistence of these seemingly contradictory flow properties.

Conclusions:

  • The assumption that monotonic RG functions preclude cyclic coupling trajectories is not universally valid.
  • Multivaluedness in RG flow functions offers a pathway for cyclic behaviors to occur alongside monotonic trends.
  • This finding has implications for understanding complex dynamics in quantum field theory and related fields.