Two-loop renormalization of the matter superfields and finiteness of N $$ \mathcal{N} $$ = 1 supersymmetric gauge theor
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Springer
Received: April 6, 2020 Accepted: May 22, 2020 Published: June 16, 2020
A.E. Kazantseva and K.V. Stepanyantzb a
Moscow State University, Faculty of Physics, Department of Quantum Theory and High Energy Physics, 119991, Moscow, Russia b Moscow State University, Faculty of Physics, Department of Theoretical Physics, 119991, Moscow, Russia
E-mail: [email protected], [email protected] Abstract: The two-loop anomalous dimension of the chiral matter superfields is calculated for a general N = 1 supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of the bare couplings, and the one defined in terms of the renormalized couplings for an arbitrary renormalization prescription. For the one-loop finite theories we find a simple relation between the higher derivative regulators under which the anomalous dimension defined in terms of the bare couplings vanishes in the considered approximation. In this case the one-loop finite theory is also two-loop finite in the HD+MSL scheme. Using the assumption that with the higher covariant derivative regularization the NSVZ equation is satisfied for RGFs defined in terms of the bare couplings, we construct the expression for the three-loop β-function. Again, the result is written both for the β-function defined in terms of the bare couplings and for the one defined in terms of the renormalized couplings for an arbitrary renormalization prescription. Keywords: Renormalization Group, Renormalization Regularization and Renormalons, Supersymmetric Gauge Theory ArXiv ePrint: 2004.00330
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)108
JHEP06(2020)108
Two-loop renormalization of the matter superfields and finiteness of N = 1 supersymmetric gauge theories regularized by higher derivatives
Contents 1 Introduction
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2 The theory under consideration
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3 Two-loop anomalous dimension
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5 Three-loop β-function 5.1 The β-function defined in terms of the bare couplings 5.2 The β-function defined in terms of the renormalized couplings
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6 Conclusion
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A Calculation of the loop integrals giving the two-loop anomalous dimension 22
1
Introduction
Quantum properties of supersymmetric theories have a lot of very interesting features. The maximally extended N = 4 supersymmetric Yang-Mills theory (SYM) is finite in all loops [1–4], while N = 2 supersymmetric gauge theories are finite beyond the one-loop approximation [1, 4, 5]. This implies that N = 2 theories finite in the one-loop approximation are also finite in all orders [6]. The one-loop finiteness can be achieved by a special choice of a gauge group and a representation for the matter superfields. In N = 1 supersymmetric theories the divergent quantum corrections can exist in all orders. However, supersymmetry leads to some interesting relations between various renormalization constants. For example, due to the finiteness of the superpotential [7] the renormalizations of masses and Yukawa coup
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