Abstract
We compute the Sd partition function of the fixed point of non-abelian gauge theories in continuous d, using the ϵ-expansion around d = 4. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in d > 4 or d < 4. In the first case we extrapolate to d = 5 to test a recently proposed construction of the UV fixed point of 5d SU(2) Yang-Mills via a susy-breaking deformation of the E1 SCFT. We find that the F theorem allows the proposed RG flow. In the second case we extrapolate to d = 3 to test whether QCD3 with gauge group SU(nc) and nf fundamental matter fields flows to a CFT or to a symmetry-breaking case. We find that within the regime with a real gauge coupling near d = 4 the CFT phase is always favored. For lower values of nf we compare the average of F between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value \( {n}_f^{\ast } \) below which the symmetry-breaking phase takes over.
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De Cesare, F., Di Pietro, L. & Serone, M. Free energy on the sphere for non-abelian gauge theories. J. High Energ. Phys. 2023, 99 (2023). https://doi.org/10.1007/JHEP04(2023)099
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DOI: https://doi.org/10.1007/JHEP04(2023)099