Abstract
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the β-functions via a gradient flow equation involving a positive definite metric. We construct the a-function at four-loop order for a general gauge theory with fermions and scalars, using only one and two loop β-functions; we are then able to provide a stringent consistency check on the general three-loop gauge β-function. In the case of an \( \mathcal{N}=1 \) supersymmetric gauge theory, we present a general condition on the chiral field anomalous dimension which guarantees an exact all-orders expression for the a-function; and we verify this up to fifth order (corresponding to the three-loop anomalous dimension).
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Jack, I., Poole, C. The a-function for gauge theories. J. High Energ. Phys. 2015, 138 (2015). https://doi.org/10.1007/JHEP01(2015)138
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DOI: https://doi.org/10.1007/JHEP01(2015)138