Gluonic evanescent operators: two-loop anomalous dimensions
arXiv:2208.08976 · doi:10.1007/JHEP02(2023)039
Abstract
Evanescent operators are a special class of operators that vanish in four-dimensional spacetime but are non-zero in dimensions. In this paper, we continue our systematic study of the evanescent operators in the pure Yang-Mills theory and focus on their two-loop renormalization. We develop an efficient strategy to compute the two-loop divergences of form factors of high-dimensional and high-length operators by combining the -dimensional unitarity method and the improved tensor reduction techniques. Two-loop anomalous dimensions are obtained for the mass-dimension-10 basis in the planar YM theory, for which both the scheme and the finite-renormalization scheme are used. We verify that the two-loop anomalous dimensions are the same in these two schemes at the Wilson-Fisher conformal fixed point. Our computation shows that the evanescent operators are indispensable in order to obtain the correct two-loop anomalous dimensions. This work provides a first computation of the two-loop anomalous dimensions of the complete set of dimension-10 operators. The method we use is also expected to provide an efficient strategy for the two-loop renormalization of general high-dimensional operators.
v2: 43 pages, 4 figures, 1 table; reference added, minor corrections
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