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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

One-Loop QCD β Function as an Index.

Roland Bittleston1, Kevin Costello1

  • 1Perimeter Institute for Theoretical Physics, 31 Caroline Street, Waterloo, Ontario, Canada.

Physical Review Letters
|June 12, 2026
PubMed
Summary
This summary is machine-generated.

Researchers derived the one-loop Quantum Chromodynamics (QCD) beta function using an index theorem in twistor space. This method connects gauge theory, theta angles, and scale invariance anomalies for novel insights.

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Last Updated: Jun 14, 2026

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07:46

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Published on: November 15, 2013

Area of Science:

  • Theoretical Physics
  • Quantum Field Theory

Background:

  • The QCD beta function describes how coupling constants change with energy scale.
  • Self-dual gauge theories and their properties are crucial in understanding quantum field theories.
  • Twistor space offers a unique geometric framework for studying field theories.

Purpose of the Study:

  • To demonstrate a novel method for calculating the one-loop QCD beta function.
  • To establish a connection between index theorems on twistor space and quantum chromodynamics.
  • To explore the relationship between theta angles in gauge theories and scale invariance.

Main Methods:

  • Utilizing an index theorem on twistor space.
  • Reformulating self-dual gauge theory as a holomorphic theory.
  • Computing the flow of the theta angle as an anomaly to scale invariance.

Main Results:

  • Successfully obtained the one-loop QCD beta function from twistor space.
  • Showed that the theta angle in self-dual gauge theory flows according to the one-loop beta function.
  • Recovered the one-loop Weyl anomaly coefficients (a-c) using the same framework.

Conclusions:

  • The index theorem on twistor space provides a powerful tool for deriving key quantities in Quantum Chromodynamics.
  • This approach offers a new perspective on the relationship between geometry, anomalies, and renormalization group flow.
  • The methodology can be extended to recover other important coefficients in quantum field theory.