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String-inspired methods and the worldline formalism in curved space

  • Olindo CorradiniEmail author
  • Maurizio Muratori
Open Access
Regular Article

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.

Notes

Acknowledgments

Open Access funding provided by Max Planck Society.

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Copyright information

© The Author(s) 2018

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.

Authors and Affiliations

  1. 1.Dipartimento di Scienze Fisiche, Informatiche e MatematicheUniversità di Modena e Reggio EmiliaModenaItaly
  2. 2.INFNSezione di BolognaBolognaItaly
  3. 3.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-Institut Am Mühlenberg 1GolmGermany

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