Abstract.
The worldline approach to Quantum Field Theory (QFT) allows to efficiently compute several quantities, such as one-loop effective actions, scattering amplitudes and anomalies, which are linked to particle path integrals on the circle. A helpful tool in the worldline formalism on the circle are string-inspired (SI) Feynman rules, which correspond to a specific way of factoring out a zero mode. In flat space this is known to generate no difficulties. In curved space, it was shown how to correctly achieve the zero mode factorization by applying BRST techniques to fix a shift symmetry. Using special coordinate systems, such as Riemann Normal Coordinates, implies the appearance of a non-linear map --originally introduced by Friedan-- which must be taken care of in order to obtain the correct results. In particular, employing SI Feynman rules, the map introduces further interactions in the worldline path integrals. In the present paper, we compute in closed form Friedan’s map for RNC coordinates in maximally symmetric spaces, and test the path integral model by computing trace anomalies. Our findings match known results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.P. Feynman, Phys. Rev. 80, 440 (1950)
L. Alvarez-Gaume, Commun. Math. Phys. 90, 161 (1983)
L. Alvarez-Gaume, E. Witten, Nucl. Phys. B 234, 269 (1984)
D. Friedan, P. Windey, Nucl. Phys. B 235, 395 (1984)
F. Bastianelli, P. van Nieuwenhuizen, Nucl. Phys. B 389, 53 (1993) hep-th/9208059
F. Bastianelli, Nucl. Phys. B 376, 113 (1992) hep-th/9112035
Z. Bern, D.A. Kosower, Phys. Rev. Lett. 66, 1669 (1991)
M.J. Strassler, Nucl. Phys. B 385, 145 (1992) hep-ph/9205205
C. Schubert, Phys. Rep. 355, 73 (2001) hep-th/0101036
M.G. Schmidt, C. Schubert, Phys. Rev. D 53, 2150 (1996) hep-th/9410100
K. Daikouji, M. Shino, Y. Sumino, Phys. Rev. D 53, 4598 (1996) hep-ph/9508377
N. Ahmadiniaz, F. Bastianelli, O. Corradini, Phys. Rev. D 93, 025035 (2016) 93
F. Bastianelli, A. Zirotti, Nucl. Phys. B 642, 372 (2002) hep-th/0205182
F. Bastianelli, O. Corradini, A. Zirotti, Phys. Rev. D 67, 104009 (2003) hep-th/0211134
F. Bastianelli, P. Benincasa, S. Giombi, JHEP 04, 010 (2005) hep-th/0503155
F. Bastianelli, C. Schubert, JHEP 02, 069 (2005) gr-qc/0412095
F. Bastianelli, O. Corradini, E. Latini, JHEP 02, 072 (2007) hep-th/0701055
F. Bastianelli, O. Corradini, E. Latini, JHEP 11, 054 (2008) arXiv:0810.0188 [hep-th]
O. Corradini, JHEP 09, 113 (2010) arXiv:1006.4452 [hep-th]
F. Bastianelli, R. Bonezzi, O. Corradini, E. Latini, JHEP 12, 113 (2012) arXiv:1210.4649 [hep-th]
P. Dai, Y.-t. Huang, W. Siegel, JHEP 10, 027 (2008) arXiv:0807.0391 [hep-th]
F. Bastianelli, R. Bonezzi, O. Corradini, E. Latini, JHEP 10, 098 (2013) arXiv:1309.1608 [hep-th]
Y. Kiem, S.J. Rey, H.T. Sato, J.T. Yee, Eur. Phys. J. C 22, 757 (2002) hep-th/0107106
R. Bonezzi, O. Corradini, S.A. Franchino Vinas, P.A.G. Pisani, J. Phys. A 45, 405401 (2012) arXiv:1204.1013 [hep-th]
P. Mansfield, Phys. Lett. B 743, 353 (2015) arXiv:1410.7298 [hep-ph]
J.P. Edwards, Phys. Lett. B 750, 312 (2015) arXiv:1411.6540 [hep-th]
F. Bastianelli, O. Corradini, P.A.G. Pisani, JHEP 02, 059 (2007) hep-th/0612236
F. Bastianelli, O. Corradini, P.A.G. Pisani, C. Schubert, JHEP 10, 095 (2008) arXiv:0809.0652 [hep-th]
F. Bastianelli, P. van Nieuwenhuizen, Path integrals and anomalies in curved space (Cambridge University Press, 2009) https://doi.org/10.1017/CBO9780511535031
F. Bastianelli, R. Bonezzi, O. Corradini, E. Latini, JHEP 06, 023 (2011) arXiv:1103.3993 [hep-th]
D.H. Friedan, Ann. Phys. 163, 318 (1985)
K. Fujikawa, Phys. Rev. Lett. 44, 1733 (1980)
F. Bastianelli, O. Corradini, P. van Nieuwenhuizen, Phys. Lett. B 494, 161 (2000) hep-th/0008045
H. Kleinert, A. Chervyakov, Phys. Lett. B 464, 257 (1999) hep-th/9906156
F. Bastianelli, O. Corradini, A. Zirotti, JHEP 01, 023 (2004) hep-th/0312064
F. Bastianelli, N.D. Hari Dass, Phys. Rev. D 64, 047701 (2001) hep-th/0104234
M.B. Green, J.G. Russo, P. Vanhove, JHEP 07, 126 (2008) arXiv:0807.0389 [hep-th]
A. Basu, Phys. Lett. B 782, 570 (2018) arXiv:1803.08329 [hep-th]
J. Guven, Phys. Rev. D 37, 2182 (1988)
F. Bastianelli, O. Corradini, E. Vassura, JHEP 04, 050 (2017) arXiv:1702.04247 [hep-th]
F. Bastianelli, O. Corradini, Eur. Phys. J. C 77, 731 (2017) arXiv:1708.03557 [hep-th]
F. Bastianelli, O. Corradini, L. Iacconi, JHEP 05, 010 (2018) arXiv:1802.05989 [hep-th]
Acknowledgments
Open Access funding provided by Max Planck Society.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Corradini, O., Muratori, M. String-inspired methods and the worldline formalism in curved space. Eur. Phys. J. Plus 133, 457 (2018). https://doi.org/10.1140/epjp/i2018-12293-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2018-12293-5