Non-renormalization of the $V\bar cc$-vertices in ${\cal N}=1$ supersymmetric theories

TL;DR

This paper proves that certain ghost vertices in ${ m f N}=1$ supersymmetric gauge theories are not renormalized at any loop order, using Slavnov--Taylor identities and explicit one-loop calculations, and relates this to the NSVZ beta-function.

Contribution

It establishes non-renormalization of specific ghost vertices in ${ m f N}=1$ supersymmetric theories and derives an exact NSVZ beta-function expression based on this.

Findings

Ghost vertices with a quantum gauge superfield are not renormalized at all loops.

Explicit one-loop calculations confirm the non-renormalization.

The NSVZ beta-function is expressed in terms of ghost and gauge superfield anomalous dimensions.

Abstract

Using the Slavnov--Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in ${\cal N}=1$ supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant derivative regularization. Using the restrictions to the renormalization constants which are imposed by the non-renormalization of the considered vertices we express the exact NSVZ $\beta$-function in terms of the anomalous dimensions of the Faddeev--Popov ghosts and of the quantum gauge superfield. In the expression for the NSVZ $\beta$-function obtained in this way the contributions of the Faddeev--Popov ghosts and of the matter superfields have the same structure.