Finite Size Effects from General Covariance and Weyl Anomaly

By exploiting the diffeomorphism invariance we relate the finite size effects of massless theories to their Weyl anomaly. We show that the universal contributions to the finite size effects are determined by certain coefficient functions in the heat kernel expansion of the related wave operators. Fo...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Dettki, Arne, Wipf, Andreas W
Format: Article
Language:English
Subjects:
Deformation effects
Isomorphism
Scalars
Size effects
Thermal expansion
Online Access:Get full text
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Summary:By exploiting the diffeomorphism invariance we relate the finite size effects of massless theories to their Weyl anomaly. We show that the universal contributions to the finite size effects are determined by certain coefficient functions in the heat kernel expansion of the related wave operators. For massless scalars confined in a \(4\)-dimensional curved spacetime with boundary the relevant coefficients are given -- confirming the results of Moss and Dowker and also of Branson and Gilkey. We apply the general results to theories on bounded regions in two- and four-dimensional flat space-times and determine the change of the effective action under arbitrary conformal deformations of the regions.
ISSN:2331-8422
DOI:10.48550/arxiv.2201.04474