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  • Letter
  • Open Access

Defects, rigid holography, and C-theorems

I. Carreño Bolla1,2, Diego Rodriguez-Gomez1,2, and J. G. Russo3,4

  • 1Department of Physics, Universidad de Oviedo, C/ Federico García Lorca 18, 33007 Oviedo, Spain
  • 2Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), C/ de la Independencia 13, 33004 Oviedo, Spain
  • 3Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluis Companys, 23, 08010 Barcelona, Spain
  • 4Departament de Física Cuántica i Astrofísica and Institut de Ciències del Cosmos, Universitat de Barcelona, Martí Franquès, 1, 08028 Barcelona, Spain

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Phys. Rev. D 108, L041701 – Published 10 August, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L041701

Abstract

We consider a general unitary scalar conformal field theory with a linear defect in D=4−ε and a surface defect in D=6−ε. Using holography and the Hamilton-Jacobi formalism, we show that the β functions controlling the defect renormalization group (RG) flow are the gradient of the entropy function. This allows the proof that the relevant C-functions decrease monotonically along the RG flow. We provide evidence that this property also holds in the full quantum theory for general scalar field theories. An obstruction to the gradient property seems to appear at two-loop order when fermions are added.

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Phys. Rev. D 108, L041701– Published 10 August, 2023
  • Received 30 June 2023
  • Accepted 26 July 2023
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