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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.24799 |
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| _version_ | 1866915891671728128 |
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| author | Ünsal, Mithat |
| author_facet | Ünsal, Mithat |
| contents | We investigate the renormalization group flow and beta functions of Yang-Mills theory and adjoint QCD in a strong, stable, self-dual background field $F$. In deep UV, theory runs according to the standard beta function, $β_0$. Treating the background as a superselection sector, we find that the theory abelianizes below the scale $\sqrt{F}$ and remains strictly abelian in the deep infrared. In the intermediate weakly-coupled regime ($Λ_{\rm YM} \ll μ\lesssim \sqrt{F}$), the gauge coupling remarkably continues to run despite the absence of propagating charged degrees of freedom. Because all non-zero Landau levels decouple, this running is driven exclusively by exact zero modes, resulting in an integer-quantized beta function coefficient, $\widetilde β_0$. Finally, we conjecture that this abelian dynamics is governed by an emergent non-commutative effective field theory that is free of pathological UV/IR mixing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24799 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantization of Beta Functions in Self-Dual Backgrounds and Emergent Non-Commutative EFT Ünsal, Mithat High Energy Physics - Theory We investigate the renormalization group flow and beta functions of Yang-Mills theory and adjoint QCD in a strong, stable, self-dual background field $F$. In deep UV, theory runs according to the standard beta function, $β_0$. Treating the background as a superselection sector, we find that the theory abelianizes below the scale $\sqrt{F}$ and remains strictly abelian in the deep infrared. In the intermediate weakly-coupled regime ($Λ_{\rm YM} \ll μ\lesssim \sqrt{F}$), the gauge coupling remarkably continues to run despite the absence of propagating charged degrees of freedom. Because all non-zero Landau levels decouple, this running is driven exclusively by exact zero modes, resulting in an integer-quantized beta function coefficient, $\widetilde β_0$. Finally, we conjecture that this abelian dynamics is governed by an emergent non-commutative effective field theory that is free of pathological UV/IR mixing. |
| title | Quantization of Beta Functions in Self-Dual Backgrounds and Emergent Non-Commutative EFT |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.24799 |