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arXiv · 2111.04031

Finiteness of the triple gauge-ghost vertices in ${\cal N}=1$ supersymmetric gauge theories: the two-loop verification

Mikhail Kuzmichev·Nikolai Meshcheriakov·Sergey Novgorodtsev·Victoria Shatalova·Ilya Shirokov·Konstantin Stepanyantz
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Abstract

By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable ${\cal N}=1$ 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 ${\cal N}=1$ supersymmetric way with the help of ${\cal N}=1$ 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.

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Mikhail Kuzmichev, Nikolai Meshcheriakov, Sergey Novgorodtsev, Victoria Shatalova, Ilya Shirokov, Konstantin Stepanyantz. 2021-11-07. Finiteness of the triple gauge-ghost vertices in ${\cal N}=1$ supersymmetric gauge theories: the two-loop verification. https://doi.org/10.1140/epjc%2Fs10052-021-09934-8

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