Free energy and defect C-theorem in free scalar theory
Abstract We describe conformal defects of p dimensions in a free scalar theory on a d-dimensional flat space as boundary conditions on the conformally flat space ℍ p+1 × 𝕊 d−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ℍ p+1 whic...
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Online Access: | https://doi.org/10.1007/JHEP05(2021)074 |
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doaj-78cdfb2e8e7c4b798b5976a873bbc0152021-05-16T11:06:33ZengSpringerOpenJournal of High Energy Physics1029-84792021-05-012021515610.1007/JHEP05(2021)074Free energy and defect C-theorem in free scalar theoryTatsuma Nishioka0Yoshiki Sato1Yukawa Institute for Theoretical Physics, Kyoto UniversityPhysics Division, National Center for Theoretical Sciences, National Tsing-Hua UniversityAbstract We describe conformal defects of p dimensions in a free scalar theory on a d-dimensional flat space as boundary conditions on the conformally flat space ℍ p+1 × 𝕊 d−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ℍ p+1 which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on ℍ p+1 × 𝕊 d−p−1 between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured C-theorem in defect CFTs.https://doi.org/10.1007/JHEP05(2021)074Conformal Field TheoryAnomalies in Field and String TheoriesRenormalization Group |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Tatsuma Nishioka Yoshiki Sato |
spellingShingle |
Tatsuma Nishioka Yoshiki Sato Free energy and defect C-theorem in free scalar theory Journal of High Energy Physics Conformal Field Theory Anomalies in Field and String Theories Renormalization Group |
author_facet |
Tatsuma Nishioka Yoshiki Sato |
author_sort |
Tatsuma Nishioka |
title |
Free energy and defect C-theorem in free scalar theory |
title_short |
Free energy and defect C-theorem in free scalar theory |
title_full |
Free energy and defect C-theorem in free scalar theory |
title_fullStr |
Free energy and defect C-theorem in free scalar theory |
title_full_unstemmed |
Free energy and defect C-theorem in free scalar theory |
title_sort |
free energy and defect c-theorem in free scalar theory |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-05-01 |
description |
Abstract We describe conformal defects of p dimensions in a free scalar theory on a d-dimensional flat space as boundary conditions on the conformally flat space ℍ p+1 × 𝕊 d−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ℍ p+1 which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on ℍ p+1 × 𝕊 d−p−1 between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured C-theorem in defect CFTs. |
topic |
Conformal Field Theory Anomalies in Field and String Theories Renormalization Group |
url |
https://doi.org/10.1007/JHEP05(2021)074 |
work_keys_str_mv |
AT tatsumanishioka freeenergyanddefectctheoreminfreescalartheory AT yoshikisato freeenergyanddefectctheoreminfreescalartheory |
_version_ |
1721439817965764608 |