The One-Loop QCD ${\hat{I}}^2$-Function as an Index

Abstract

In this letter we show that the one-loop QCD ${\hat{I}}^2$-function can be obtained from an index theorem on twistor space. This is achieved by recalling that the $\hat{I}¸$-angle of self-dual gauge theory flows according the one-loop ${\hat{I}}^2$-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.

7 pages + 2 pages supplementary material; v2: references added, typos corrected; v3: published in PRL