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One-Loop QCD β Function as an Index

Roland Bittleston* and Kevin Costello

  • *Contact author rbittleston@perimeterinstitute.ca
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Phys. Rev. Lett. 136, 211601 – Published 29 May, 2026

DOI: https://doi.org/10.1103/5kd5-3724

Abstract

In this Letter, we show that the one-loop QCD β function can be obtained from an index theorem on twistor space. This is achieved by recalling that the θ angle of self-dual gauge theory flows according the one-loop β function. Rewriting self-dual gauge theory as a holomorphic theory on twistor space this flow can be computed as the anomaly to scale invariance. The one-loop Weyl anomaly coefficient a−c can be recovered similarly.

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Phys. Rev. Lett. 136, 211601– Published 29 May, 2026
  • Received 24 November 2025
  • Accepted 30 April 2026
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