Abstract
We compute the Schwinger terms in the energy-momentum tensor commutator algebra from the anomalies present in Weyl-invariant and diffeomorphism-invariant effective actions for two dimensional massless scalar fields in a gravitational background. We find that the Schwinger terms are not sensitive to the regularization procedure and that they are independent of the background metric.
Highlights
The theory of a scalar field coupled to gravity has to follow an ad-hoc prescription: the functional integration over the scalar field φ involves the evaluation of a determinant of the Laplace operator, which is ambiguous
In this paper we investigate this question and find that, the anomalous commutators coincide in both versions of the theory and lead to the well known result from Conformal Field Theory [9]
We do this calculation both for flat and curved space-time. In the latter case of general metric the computation is done without any gauge fixing; this is the proper procedure because gauge fixing would be in conflict with the Weyl-invariant regularization, that breaks diffeomorphism invariance
Summary
The theory of a (quantized) scalar field coupled to gravity has to follow an ad-hoc prescription: the functional integration over the scalar field φ involves the evaluation of a determinant of the Laplace operator, which is ambiguous. For massless scalar fields in two-dimensional space-time the standard prescription implements a diffeomorphism invariant regularization that leads to the well known Polyakov action [1] ΓP[gμν], a functional of the background metric gμν that is diffeomorphism invariant but has an ( well known) anomaly with respect to Weyl transformations. In this paper we investigate this question and find that, the anomalous commutators coincide in both versions of the theory and lead to the well known result from Conformal Field Theory [9]. We do this calculation both for flat and curved space-time. The results, when properly interpreted, lead to the same Schwinger terms as in the flat space-time and, show that the Schwinger terms do not depend on the curvature
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
