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arXiv · 2310.13109

The four-loop $\beta$-function from vacuum supergraphs and the NSVZ relation for ${\cal N}=1$ SQED regularized by higher derivatives

Ilya Shirokov·Valentina Shirokova
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Abstract

In ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives we obtain the four-loop beta function using a method based on calculating vacuum supergraphs. For this purpose we use a special C++ program which obtain contributions to the $\beta$-function from supergraphs without external legs in the form of integrals of double total derivatives. After that the result was compared with the three-loop anomalous dimension calculated earlier. We explicitly check the NSVZ relation in this order.

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Ilya Shirokov, Valentina Shirokova. 2023-10-19. The four-loop $\beta$-function from vacuum supergraphs and the NSVZ relation for ${\cal N}=1$ SQED regularized by higher derivatives. https://doi.org/10.1140/epjc%2Fs10052-024-12587-y

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