Geodesic
The NSVZ $\beta$-function in supersymmetric theories with different
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 475-486 Cet article a éte moissonné depuis la source Math-Net.Ru

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We briefly review the calculations of quantum corrections related to the exact Novikov–Shifman–Vainshtein–Zakharov (NSVZ) $\beta$-function in $\mathcal{N}=1$ supersymmetric theories, paying special attention to the scheme dependence of the results. We explain how the NSVZ relation is obtained for the renormalization group functions defined in terms of the bare coupling constant if a theory is regularized by higher derivatives. We also describe how to construct a special renormalization prescription that gives the NSVZ relation for the renormalization group functions defined in terms of the renormalized coupling constant exactly in all orders for Abelian supersymmetric theories regularized by higher derivatives and discuss the scheme dependence of the NSVZ $\beta$-function (for the renormalization group functions defined in terms of the renormalized coupling constant) in the non-Abelian case. We show that in this case, the NSVZ $\beta$-function leads to a certain scheme-independent equality.
Keywords: supersymmetry, renormalization, $\beta$-function. 
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A. L. Kataev; K. V. Stepanyantz. The NSVZ $\beta$-function in supersymmetric theories with different. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 3, pp. 475-486. http://geodesic.mathdoc.fr/item/TMF_2014_181_3_a4/

[1] V. A. Novikov, M. A. Shifman, A. I. Vainshtein, V. I. Zakharov, Nucl. Phys. B, 229:2 (1983), 381–393 | DOI

[2] A. I. Vainshtein, V. I. Zakharov, V. A. Novikov, M. A. Shifman, YaF, 43:6 (1986), 1596–1605

[3] M. A. Shifman, A. I. Vainshtein, “Instantons versus supersymmetry: fifteen years later”: M. A. Shifman, ITEP Lectures on Particle Physics and Field Theory, World Scientific Lecture Notes in Physics, 62, World Sci., Singapore, 1999, 485–647, arXiv: hep-th/9902018 | DOI | MR | Zbl

[4] D. R. T. Jones, Phys. Lett. B, 123:1–2 (1983), 45–46 | DOI | MR

[5] A. I. Vainshtein, M. A. Shifman, ZhETF, 91:3 (1986), 723–744 | MR

[6] N. Arkani-Hamed, H. Murayama, JHEP, 06 (2000), 030, 44 pp., arXiv: arXiv:hep-th/9707133 | DOI | Zbl

[7] A. I. Vainshtein, V. I. Zakharov, M. A. Shifman, Pisma ZhETF, 42:4 (1985), 182–184

[8] M. A. Shifman, A. I. Vainshtein, V. I. Zakharov, Phys. Lett. B, 166:3 (1986), 334–336 | DOI

[9] E. Kraus, C. Rupp, K. Sibold, Nucl. Phys. B, 661:1–2 (2003), 83–98 | DOI | MR | Zbl

[10] J. C. Taylor, Nucl. Phys. B, 33:2 (1971), 436–444 | DOI | MR

[11] A. A. Slavnov, TMF, 10:2 (1972), 153–161 | DOI

[12] I. L. Buchbinder, K. V. Stepanyantz, Nucl. Phys. B, 883 (2014), 20–44 | DOI | MR | Zbl

[13] J. Hisano, M. A. Shifman, Phys. Rev. D, 56:8 (1997), 5475–5482, arXiv: hep-ph/9705417 | DOI | MR

[14] I. Jack, D. R. T. Jones, Phys. Lett. B, 415:4 (1997), 383–389, arXiv: hep-ph/9709364 | DOI | MR

[15] L. V. Avdeev, D. I. Kazakov, I. N. Kondrashuk, Nucl. Phys. B, 510:1 (1998), 289–312, arXiv: hep-ph/9709397 | DOI | MR | Zbl

[16] A. A. Slavnov, Nucl. Phys. B, 31:2 (1971), 301–305 | DOI | MR

[17] A. A. Slavnov, TMF, 13:2 (1972), 174–177 | DOI

[18] A. I. Vainshtein, V. I. Zakharov, M. A. Shifman, YaF, 43:2 (1986), 1596–1605

[19] A. A. Slavnov, L. D. Faddeev, Vvedenie v kvantovuyu teoriyu kalibrovochnykh polei, Nauka, M., 1978 | MR | Zbl

[20] V. K. Krivoschekov, TMF, 36:3 (1978), 291–302 | DOI | MR

[21] P. C. West, Nucl. Phys. B, 268:1 (1986), 113–124 | DOI | MR

[22] C. P. Martin, F. Ruiz Ruiz, Nucl. Phys. B, 436:3 (1995), 545–581 | DOI

[23] D. J. Gross, F. Wilczek, Phys. Rev. Lett., 30:26 (1973), 1343–1346 | DOI

[24] H. D. Politzer, Phys. Rev. Lett., 30:26 (1973), 1346–1349 | DOI

[25] M. Asorey, F. Falceto, Phys. Rev. D, 54:8 (1996), 5290–5301, arXiv: hep-th/9502025 | DOI | MR

[26] T. D. Bakeyev, A. A. Slavnov, Modern Phys. Lett. A, 11:19 (1996), 1539–1554 | DOI

[27] P. I. Pronin, K. V. Stepanyantz, Phys. Lett. B, 414:1–2 (1997), 117–122 | DOI

[28] A. A. Soloshenko, K. V. Stepanyants, TMF, 140:3 (2004), 437–459 | DOI | DOI | Zbl

[29] A. B. Pimenov, E. S. Shevtsova, K. V. Stepanyantz, Phys. Lett. B, 686:4–5 (2010), 293–297, arXiv: 0912.5191 | DOI | MR

[30] A. V. Smilga, A. Vainshtein, Nucl. Phys. B, 704:3 (2005), 445–474, arXiv: hep-th/0405142 | DOI | MR | Zbl

[31] K. V. Stepanyantz, Factorization of integrals defining the two-loop $\beta$-function for the general renormalizable $N=1$ SYM theory, regularized by the higher covariant derivatives, into integrals of double total derivatives, arXiv: 1108.1491

[32] K. V. Stepanyantz, Nucl. Phys. B, 852:1 (2011), 71–107, arXiv: 1102.3772 | DOI | MR | Zbl

[33] K. V. Stepanyantz, JHEP, 08 (2014), 096, 77 pp., arXiv: 1404.6717 | DOI

[34] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1984 | MR

[35] G. 't Hooft, M. Veltman, Nucl. Phys. B, 44:1 (1972), 189–213 | DOI | MR

[36] C. G. Bollini, J. J. Giambiagi, Nuovo Cimento B, 12 (1972), 20–26

[37] J. F. Ashmore, Lett. Nuovo Cimento, 4:8 (1972), 289–290 | DOI

[38] G. M. Cicuta, E. Montaldi, Lett. Nuovo Cimento Ser. 2, 4:9 (1972), 329–332 | DOI

[39] S. Ferrara, B. Zumino, Nucl. Phys. B, 79:3 (1974), 413–421 | DOI | MR

[40] D. R. T. Jones, Nucl. Phys. B, 87:1 (1975), 127–132 | DOI | MR

[41] W. Siegel, Phys. Lett. B, 84:2 (1979), 193–196 | DOI | MR

[42] A. A. Slavnov, Phys. Lett. B, 518:1–2 (2001), 195–200 | DOI | Zbl

[43] A. A. Slavnov, TMF, 132:3 (2002), 434–448 | DOI | DOI | MR | Zbl

[44] A. A. Slavnov, K. V. Stepanyants, TMF, 135:2 (2003), 265–279 | DOI | DOI | Zbl

[45] A. A. Slavnov, K. V. Stepanyants, TMF, 139:2 (2004), 179–191 | DOI | DOI | Zbl

[46] W. Siegel, Phys. Lett. B, 94:1 (1980), 37–40 | DOI | MR

[47] L. V. Avdeev, G. A. Chochia, A. A. Vladimirov, Phys. Lett. B, 105:4 (1981), 272–274 | DOI

[48] L. V. Avdeev, A. A. Vladimirov, Nucl. Phys. B, 219:1 (1983), 262–276 | DOI

[49] W. A. Bardeen, A. J. Buras, D. W. Duke, T. Muta, Phys. Rev. D, 18:11 (1978), 3998–4017 | DOI

[50] L. V. Avdeev, O. V. Tarasov, Phys. Lett. B, 112:4–5 (1982), 356–358 | DOI

[51] V. N. Velizhanin, Phys. Lett. B, 696:5 (2011), 560–562 | DOI | MR

[52] L. V. Avdeev, Phys. Lett. B, 117:5 (1982), 317–320 | DOI

[53] V. N. Velizhanin, Nucl. Phys. B, 818:1 (2009), 95–100, arXiv: 0809.2509 | DOI | MR | Zbl

[54] I. Jack, D. R. T. Jones, C. G. North, Phys. Lett. B, 386:1 (1996), 138–140 | DOI

[55] R. V. Harlander, D. R. T. Jones, P. Kant, L. Mihaila, M. Steinhauser, JHEP, 12 (2006), 024, 13 pp. | DOI | MR | Zbl

[56] I. Jack, D. R. T. Jones, P. Kant, L. Mihaila, JHEP, 09 (2007), 058, 40 pp. | DOI

[57] L. Mihaila, Adv. High Energy Phys., 2013 (2013), 607807, 64 pp. | DOI | MR | Zbl

[58] T. A. Ryttov, R. Shrock, Phys. Rev. D, 85:7 (2012), 076009, 16 pp. | DOI

[59] I. Jack, D. R. T. Jones, C. G. North, Nucl. Phys. B, 486:1 (1997), 479–499, arXiv: hep-ph/9609325 | DOI

[60] I. Jack, D. R. T. Jones, A. Pickering, Phys. Lett. B, 435:1–2 (1998), 61–66 | DOI

[61] J. Mas, C. Seijas, M. Pérez-Victoria, JHEP, 03 (2002), 049, 20 pp., arXiv: hep-th/0202082 | DOI

[62] D. Z. Freedman, K. Johnson, J. I. Latorre, Nucl. Phys. B, 371:1–2 (1992), 353–44 | DOI | MR

[63] F. del Águila, A. Culatti, R. Muñoz Tapia, M. Pérez-Victoria, Nucl. Phys. B, 537:1–3 (1999), 561–585, arXiv: hep-ph/9806451 | DOI | MR | Zbl

[64] F. del Águila, A. Culatti, R. Muñoz-Tapia, M. Pérez-Victoria, Nucl. Phys. B, 504:1 (1997), 532–550, arXiv: hep-ph/9702342 | DOI

[65] A. I. Vainshtein, M. A. Shifman, YaF, 44 (1986), 498

[66] G. 't Hooft, Phys. Rev. D, 14:12 (1976), 3432–3450 ; Erratum, 18:6 (1978), 2199–2200 | DOI | DOI

[67] T. R. Morris, D. A. Ross, C. T. Sachrajda, Nucl. Phys. B, 264 (1986), 111–153 | DOI

[68] T. R. Morris, D. A. Ross, C. T. Sachrajda, Phys. Lett. B, 158:3 (1985), 223–226 | DOI

[69] T. R. Morris, D. A. Ross, C. T. Sachrajda, Phys. Lett. B, 172:1 (1986), 40–45 | DOI

[70] A. L. Kataev, K. V. Stepanyantz, Nucl. Phys. B, 875:2 (2013), 459–482 | DOI | MR | Zbl

[71] A. L. Kataev, K. V. Stepanyantz, Phys. Lett. B, 730 (2014), 184–198, arXiv: 1311.0589 | DOI

[72] A. A. Slavnov, TMF, 33:2 (1977), 210–217 | DOI | MR

[73] S. G. Gorishny, A. L. Kataev, S. A. Larin, L. R. Surguladze, Phys. Lett. B, 256:1 (1991), 81–85 | DOI

[74] P. A. Baikov, K. G. Chetyrkin, J. H. Kühn, J. Rittinger, JHEP, 07 (2012), 017 | DOI

[75] A. L. Kataev, S. A. Larin, Pisma v ZhETF, 96:1–2 (2012), 64–67 | DOI

[76] D. J. Broadhurst, R. Delbourgo, D. Kreimer, Phys. Lett. B, 366:1 (1996), 421–428, arXiv: hep-ph/9509296 | DOI | MR

[77] K. G. Chetyrkin, S. G. Gorishny, A. L. Kataev, S. A. Larin, F. V. Tkachov, Phys. Lett. B, 116:6 (1981), 455–458 | DOI | MR

[78] M. T. Grisaru, W. Siegel, M. Rocek, Nucl. Phys. B, 159:3 (1979), 429–450 | DOI | MR