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Challenge to the a theorem in six dimensions.

Benjamín Grinstein1, David Stone1, Andreas Stergiou2

  • 1Department of Physics, University of California, San Diego, La Jolla, California 92093, USA.

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|December 20, 2014
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Summary

In six dimensions, the a-theorem quantity a-tilde in multiflavor phi^3 theory increases monotonically, unlike in 2 or 4 dimensions. This suggests new insights are needed for the a-theorem in higher dimensions.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • The a-theorem constrains renormalization group flows in quantum field theories.
  • Previous studies established the a-theorem in two and four dimensions.
  • The Euler term's coefficient 'a' in the trace anomaly is a key component.

Purpose of the Study:

  • To investigate the validity and behavior of the a-theorem in six dimensions.
  • To analyze multiflavor phi^3 theory in higher spacetime dimensions.
  • To extend the understanding of the 'a-tilde' quantity, a generalization of the 'a' coefficient.

Main Methods:

  • Perturbation theory analysis of multiflavor phi^3 theory.
  • Calculation of anomalous dimensions and beta functions to two-loop order.
  • Application of Weyl consistency conditions for trace anomaly analysis.

Main Results:

  • The quantity a-tilde increases monotonically along renormalization group flows away from the trivial fixed point in six dimensions.
  • This behavior contrasts with findings in two and four dimensions.
  • Anomalous dimensions and beta functions for multiflavor phi^3 theory were computed up to two loops.

Conclusions:

  • The monotonic increase of a-tilde suggests a potential breakdown or modification of the standard a-theorem in six dimensions.
  • New theoretical intuition is required to reconcile these findings with existing knowledge.
  • The study highlights the importance of spacetime dimension in the context of quantum field theory theorems.