https://doi.org/10.1140/epjp/i2018-12293-5
Regular Article
String-inspired methods and the worldline formalism in curved space
1
Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, via Campi 213/A, I-41125, Modena, Italy
2
INFN, Sezione di Bologna, via Irnerio 46, I-40126, Bologna, Italy
3
Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut Am Mühlenberg 1, 14476, Golm, Germany
* e-mail: olindo.corradini@unimore.it
Received:
20
August
2018
Accepted:
4
October
2018
Published online:
9
November
2018
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.
© The Author(s), 2018
