Abstract
We study the one loop renormalisation of 4d SU(N) Yang-Mills theory with M adjoint representation scalar multiplets related by O(M) symmetry. General M are of field theoretic interest, and the 4d one loop beta function of the gauge coupling g2 vanishes for the case M = 22, which is intriguing for string theory. This case is related to D3 branes of critical bosonic string theory in D = 22 + 4 = 26. An RG fixed point could have provided a definition for a purely bosonic AdS/CFT, but we show that scalar self-couplings λ ruin one-loop conformal invariance in the large N limit. There are real fixed flows (fixed points of λ/g2) only for M ≥ 406, rendering one-loop fixed points of the gauge coupling and scalar couplings incompatible.
We develop and check an algebraic approach to the one-loop renormalisation group which we find to be characterised by a non-associative algebra of marginal couplings. In the large N limit, the resulting RG flows typically suffer from strong coupling in both the ultraviolet and the infrared. Only for M ≥ 406 fine-tuned solutions exist which are weakly coupled in the infrared.
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Acknowledgments
We wish to thank Igor Klebanov, Daniel Litim, Hugh Osborn, Fedor Popov, Francesco Sannino, Anders Eller Thomsen and Arkady Tseytlin for helpful correspondence. The work of B.S. is supported by the Swedish research council VR, contract DNR-2018-03803.
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Flodgren, N., Sundborg, B. One-loop algebras and fixed flow trajectories in adjoint multi-scalar gauge theory. J. High Energ. Phys. 2023, 129 (2023). https://doi.org/10.1007/JHEP04(2023)129
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DOI: https://doi.org/10.1007/JHEP04(2023)129