2018/04/30 by Vladimir Prochazka · 8 citations
Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Conformal anomaly #Conformal map #Curvature #Curved space #Feynman diagram #Position and momentum space #Quantum Electrodynamics and Casimir Effect #Quantum, superfluid, helium dynamics #Scalar (mathematics) #Tensor (intrinsic definition) #cond-mat.str-el #hep-th
paper · pdf · doi:10.1007/jhep10(2018)170
published in Journal of High Energy Physics 2018(10) (Springer Nature) · 25 pages, 4 figures, v2- references updated, relation to the literature discussed, presentation streamlined
openalex created_date 2018/04/13 · arxiv created 2018/09/03 · openalex publication_date 2018/10/01 · arxiv updated 2018/11/14 · openalex updated_date 2026/08/05
A bstract We study the momentum space representation of energy-momentum tensor two-point functions on a space with a planar boundary in d = 3. We show that non-conservation of momentum in the direction perpendicular to the boundary allows for new phenomena compared to the boundary-less case. Namely we demonstrate how local contact terms arise when the correlators are expanded in the regime where parallel momentum is small compared to the perpendicular one, which corresponds to the near-boundary limit. By exploring two-derivative counterterms involving components of Riemann tensor we identify a finite, scheme-independent part of the two-point function. We then relate this component to the conformal anomaly c ∂ proportional to the boundary curvature \widehatR <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>R</mml:mi> <mml:mo>^</mml:mo> </mml:mover> </mml:math> . In the formalism of this paper c ∂ arises due to integrating out bulk modes coupled to the curved space, which generate local contributions the effective action at the boundary. To calculate the anomaly in specific (free-field) examples, we combine the method of images with Feynman diagrammatic techniques and propose a general methodology for perturbative computations of this type. The framework is tested by computing c ∂ on the explicit example of free scalar with mixed boundary conditions where we find agreement with the literature.