We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time and find that dimensional regularization is a manifestly supersymmetric regularization scheme, since the classically supersymmetric action does not need any counterterm to preserve worldline supersymmetry. We apply this regularization scheme to the worldline description of Dirac fermions coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4 dimensions, providing an additional check on the regularization with finite propagation time. Then we come to the main topic and consider the one-loop effective action for a Dirac field in a gravitational background. We describe how to represent this effective action as a worldline path integral and compute explicitly the one- and two-point correlation functions, i.e. the spin 1/2 particle contribution to the graviton tadpole and graviton self-energy. These results are presented for the general case of a massive fermion. It is interesting to note that in the worldline formalism the coupling to gravity can be described entirely in terms of the metric, avoiding the introduction of a vielbein. Consequently, the fermion--graviton vertices are always linear in the graviton, just like the standard coupling of fermions to gauge fields.

Dimensional regularization for N=1supersymmetric sigma models and the worldline formalism / Bastianelli, Fiorenzo; Corradini, Olindo; Zirotti, Andrea. - In: PHYSICAL REVIEW D. - ISSN 0556-2821. - D67 (2003) 104009:(2003), pp. 1-15. [10.1103/PhysRevD.67.104009]

Dimensional regularization for N=1supersymmetric sigma models and the worldline formalism

Abstract

We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time and find that dimensional regularization is a manifestly supersymmetric regularization scheme, since the classically supersymmetric action does not need any counterterm to preserve worldline supersymmetry. We apply this regularization scheme to the worldline description of Dirac fermions coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4 dimensions, providing an additional check on the regularization with finite propagation time. Then we come to the main topic and consider the one-loop effective action for a Dirac field in a gravitational background. We describe how to represent this effective action as a worldline path integral and compute explicitly the one- and two-point correlation functions, i.e. the spin 1/2 particle contribution to the graviton tadpole and graviton self-energy. These results are presented for the general case of a massive fermion. It is interesting to note that in the worldline formalism the coupling to gravity can be described entirely in terms of the metric, avoiding the introduction of a vielbein. Consequently, the fermion--graviton vertices are always linear in the graviton, just like the standard coupling of fermions to gauge fields.
Scheda breve Scheda completa Scheda completa (DC)
D67 (2003) 104009
1
15
Dimensional regularization for N=1supersymmetric sigma models and the worldline formalism / Bastianelli, Fiorenzo; Corradini, Olindo; Zirotti, Andrea. - In: PHYSICAL REVIEW D. - ISSN 0556-2821. - D67 (2003) 104009:(2003), pp. 1-15. [10.1103/PhysRevD.67.104009]
Bastianelli, Fiorenzo; Corradini, Olindo; Zirotti, Andrea
File in questo prodotto:
File
PRD67.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Versione dell'editore (versione pubblicata)
Dimensione 172.49 kB
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11380/1074703`
• ND
• 5
• 51