Abstract
By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable {{mathcal {N}}}=1 supersymmetric gauge theory are UV finite in the two-loop approximation. For this purpose we calculate the two-loop divergent contribution to the bar{c}^+ V c-vertex proportional to (C_2)^2 and use the finiteness of the two-loop contribution proportional to C_2 T(R) which has been checked earlier. The theory under consideration is regularized by higher covariant derivatives and quantized in a manifestly {{mathcal {N}}}=1 supersymmetric way with the help of {{mathcal {N}}}=1 superspace. The two-loop finiteness of the vertices with one external line of the quantum gauge superfield and two external lines of the Faddeev–Popov ghosts has been verified for a general xi -gauge. This result agrees with the nonrenormalization theorem proved earlier in all orders, which is an important step for the all-loop derivation of the exact NSVZ beta -function.
Highlights
In supersymmetric quantum field theory models ultraviolet (UV) divergences are essentially restricted by some nonrenormalization theorems
The all-loop finiteness of the triple gauge-ghost vertices allowed to rewrite the NSVZ equation in an equivalent form [21]. It relates the β-function to the anomalous dimensions of quantum superfields. This new form of the NSVZ equation was subsequently derived by perturbative methods in all loops for renormalization group functions (RGFs) defined in terms of the bare couplings for theories regularized by higher covariant derivatives [76,102]
By an explicit calculation we have verified that the sum of the two-loop quantum corrections to the triple gauge-ghost vertices in renormalizable N = 1 supersymmetric gauge theories regularized by higher covariant derivatives is finite in the ultraviolet region
Summary
In supersymmetric quantum field theory models ultraviolet (UV) divergences are essentially restricted by some nonrenormalization theorems Cancellations of these divergences in theories with extended supersymmetry are especially impressive. The superpotential does not receive divergent quantum corrections [12], the β-function is related to the anomalous dimension of the matter superfields by the NSVZ equation [13–20], and the triple gauge-ghost vertices are finite in all loops [21]. The NSVZ-like equations describing the renormalization of the gaugino mass [31–33] can be considered as nonrenormalization theorems for the terms which softly break supersymmetry. Using these and other relations between the renormalization of soft breaking parameters and the renormalization of the rigid theory [31–38] it is possible to construct allloop finite theories with softly broken supersymmetry [37– 39].
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