Regular Article - Theoretical Physics
Exact -functions for supersymmetric theories finite in the lowest loops
Faculty of Physics, Department of Theoretical Physics, Moscow State University, 119991, Moscow, Russia
Accepted: 18 June 2021
Published online: 2 July 2021
We consider a one-loop finite supersymmetric theory in such a renormalization scheme that the first L contributions to the gauge -function and the first contributions to the anomalous dimension of the matter superfields and to the Yukawa -function vanish. It is demonstrated that in this case the NSVZ equation and the exact equation for the Yukawa -function in the first nontrivial order are valid for an arbitrary renormalization prescription respecting the above assumption. This implies that under this assumption the -loop contribution to the gauge -function and the L-loop contribution to the Yukawa -function are always expressed in terms of the L-loop contribution to the anomalous dimension of the matter superfields. This statement generalizes the result of Grisaru, Milewski, and Zanon that for a theory finite in L loops the -loop contribution to the -function also vanishes. In particular, it gives a simple explanation why their result is valid although the NSVZ equation does not hold in an arbitrary subtraction scheme.
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