Geodesic
Equation for one-loop divergences in two dimensions and its
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 505-518

Voir la notice de l'article provenant de la source Math-Net.Ru

We derive a simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space–time for theories in which the second variation of the action is a nonminimal second-order operator with small nonminimal terms. In particular, this formula allows calculating terms that are integrals of total derivatives. As an application of the result, we obtain one-loop divergences for higher-spin fields on a constant-curvature background in a nonminimal gauge that depends on two parameters. By an explicit calculation, we demonstrate that with the considered accuracy, the result is gauge independent and, moreover, spin independent for spins $s\ge3$.
Mots-clés : one-loop divergence
Keywords: higher-spin field. 
E. P. Popova; K. V. Stepanyantz. Equation for one-loop divergences in two dimensions and its. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 3, pp. 505-518. http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a6/
@article{TMF_2016_187_3_a6,
     author = {E. P. Popova and K. V. Stepanyantz},
     title = {Equation for one-loop divergences in two dimensions and its},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {505--518},
     year = {2016},
     volume = {187},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a6/}
}
TY  - JOUR
AU  - E. P. Popova
AU  - K. V. Stepanyantz
TI  - Equation for one-loop divergences in two dimensions and its
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 505
EP  - 518
VL  - 187
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a6/
LA  - ru
ID  - TMF_2016_187_3_a6
ER  - 
%0 Journal Article
%A E. P. Popova
%A K. V. Stepanyantz
%T Equation for one-loop divergences in two dimensions and its
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 505-518
%V 187
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2016_187_3_a6/
%G ru
%F TMF_2016_187_3_a6

[1] G. 't Hooft, M. Veltman, Ann. Inst. H. Poincaré Sect. A (N. S.), 20 (1974), 69–74 | MR

[2] P. I. Pronin, K. V. Stepanyantz, Nucl. Phys. B, 485:1 (1997), 517–544, arXiv: hep-th/9605206 | DOI

[3] K. A. Kazakov, P. I. Pronin, K. V. Stepanyantz, Gravit. Cosmology, 4:1 (1998), 17–27 | Zbl

[4] M. Y. Kalmykov, K. A. Kazakov, P. I. Pronin, K. V. Stepanyantz, Class. Quant. Grav., 15:12 (1998), 3777–3794, arXiv: hep-th/9809169 | DOI | MR | Zbl

[5] K. A. Kazakov, P. I. Pronin, Phys. Rev. D, 59:6 (1999), 064012, 13 pp., arXiv: hep-th/9806023 | DOI | MR

[6] K. A. Kazakov, P. I. Pronin, TMF, 121:3 (1999), 387–411 | DOI | DOI | MR | Zbl

[7] E. A. Andriyash, K. V. Stepanyants, Vestnik Mosk. un-ta. Ser. 3. Fiz. Astron., 2003, no. 2, 24–26 | Zbl

[8] D. A. Bolotin, S. V. Poslavsky, Introduction to Redberry: the computer algebra system designed for tensor manipulation, arXiv: 1302.1219

[9] S. Poslavsky, D. Bolotin, J. Phys.: Conf. Ser., 608:1 (2015), 012060, 6 pp. | DOI

[10] S. Minakshisundaram, A. Pleijel, Canadian J. Math., 1 (1949), 242–256 | DOI | MR | Zbl

[11] S. Minakshisundaram, J. Indian Math. Soc. (N. S.), 17 (1953), 158–165 | MR

[12] R. T. Seeley, “Complex powers of an elliptic operator”, Singular Integrals (University of Chicago, Chicago, IL, April 20–22, 1966), Proceedings of Symposia in Pure Mathematics, 10, ed. A. P. Calderón, AMS, Providence, RI, 1967, 288–307 | DOI | MR

[13] P. B. Gilkey, J. Diff. Geom., 10:4 (1975), 601–618 | DOI | MR | Zbl

[14] J. S. Schwinger, Phys. Rev., 82:5 (1951), 664–679 | DOI | MR | Zbl

[15] B. S. de Vitt, Dinamicheskaya teoriya grupp i polei, M., Nauka, 1987 | MR

[16] A. O. Barvinsky, G. A. Vilkovisky, Phys. Rept., 119 (1985), 1 | DOI | MR

[17] V. P. Gusynin, E. V. Gorbar, V. V. Romankov, Nucl. Phys. B, 362:1 (1991), 449–471 | DOI | MR

[18] R. Camporesi, Phys. Rep., 196:1–2 (1990), 1–134 | DOI | MR

[19] R. Camporesi, A. Higuchi, Phys. Rev. D, 47:8 (1993), 3339–3344 | DOI | MR

[20] I. L. Buchbinder, V. A. Krykhtin, H. Takata, “One-loop divergence of effective action of Higher spin theory in $AdS_4$”, talk given at the International Conference “Quantum Field Theory and Gravity” (Tomsk, July 5–9, 2010)

[21] K. Khuang, Kvarki, leptony i kalibrovochnye polya, Mir, M., 1985 | MR | MR

[22] P. I. Pronin, K. Stepanyantz, Phys. Lett. B, 414:1–2 (1997), 117–122, arXiv: hep-th/9707008 | DOI

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

[24] C. G. Bollini, J. J. Giambiagi, Nuovo Cimento B, 12:1 (1972), 20–26

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

[26] G. M. Cicuta, E. Montaldi, Lett. Nuovo Cim., 4:9 (1972), 329–332 | DOI

[27] Y. N. Obukhov, Nucl. Phys. B, 212:2 (1983), 237–254 | DOI | MR

[28] C. Fronsdal, Phys. Rev. D, 18:10 (1978), 3624–3629 | DOI

[29] J. Fang, C. Fronsdal, Phys. Rev. D, 18:10 (1978), 3630–3633 | DOI

[30] M. A. Vasiliev, Fortsch. Phys., 52:6 (2004), 702–717, arXiv: hep-th/0401177 | DOI | MR | Zbl

[31] X. Bekaert, S. Cnockaert, C. Iazeolla, M. A. Vasiliev, Nonlinear higher spin theories in various dimensions, arXiv: hep-th/0503128

[32] C. Fronsdal, Phys. Rev. D, 20:4 (1979), 848–856 | DOI | MR

[33] I. L. Buchbinder, V. A. Krykhtin, P. M. Lavrov, Modern Phys. Lett. A, 26:16 (2011), 1183–1196, arXiv: 1101.4860 | DOI | MR | Zbl

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

[35] L. D. Faddeev, V. N. Popov, Phys. Lett. B, 25:1 (1967), 29–30 | DOI

[36] R. E. Kallosh, O. V. Tarasov, I. V. Tyutin, Nucl. Phys. B, 137:1–2 (1978), 145–163 | DOI | MR

[37] E. Popova, K. V. Stepanyants, Vestnik TGPU, 13(128) (2012), 130–133