The One-Loop QCD $β$-Function as an Index
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918216470626304 |
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| author | Bittleston, Roland Costello, Kevin |
| author_facet | Bittleston, Roland Costello, Kevin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The One-Loop QCD $β$-Function as an Index Bittleston, Roland Costello, Kevin High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics 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. |
| title | The One-Loop QCD $β$-Function as an Index |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2510.26764 |