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The Poisson sigma model on closed surfaces


Bonechi, F; Cattaneo, A S; Mnëv, P (2012). The Poisson sigma model on closed surfaces. Journal of High Energy Physics, 2012(1):99.

Abstract

Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kähler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to other sigma models, at least of the AKSZ type.

Abstract

Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kähler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to other sigma models, at least of the AKSZ type.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Topological Field Theories – Field Theories in Lower Dimensions – Sigma Models
Language:English
Date:October 2012
Deposited On:14 Feb 2012 20:50
Last Modified:05 Apr 2016 15:33
Publisher:Institute of Physics Publishing
ISSN:1029-8479
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/JHEP01(2012)099
Related URLs:http://arxiv.org/abs/1110.4850

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