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Towards a C-theorem in defect CFT

  • Nozomu KobayashiEmail author
  • Tatsuma Nishioka
  • Yoshiki Sato
  • Kento Watanabe
Open Access
Regular Article - Theoretical Physics
  • 21 Downloads

Abstract

We explore a C-theorem in defect conformal field theories (DCFTs) that unify all the known conjectures and theorems until now. We examine as a candidate C-function the additional contributions from conformal defects to the sphere free energy and the entanglement entropy across a sphere in a number of examples including holographic models. We find the two quantities are equivalent, when suitably regularized, for codimension-one defects (or boundaries), but differ by a universal constant term otherwise. Moreover, we find in a few field theoretic examples that the sphere free energy decreases but the entanglement entropy increases along a certain renormalization group (RG) flow triggered by a defect localized perturbation which is assumed to have a trivial IR fixed point without defects. We hence propose a C-theorem in DCFTs stating that the increment of the regularized sphere free energy due to the defect does not increase under any defect RG flow. We also provide a proof of our proposal in several holographic models of defect RG flows.

Keywords

Conformal Field Theory AdS-CFT Correspondence Renormalization Group 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics, Faculty of ScienceThe University of TokyoTokyoJapan
  2. 2.Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced StudyThe University of TokyoKashiwaJapan

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