Operator product expansion for conformal defects
Abstract We study the operator product expansion (OPE) for scalar conformal defects of any codimension in CFT. The OPE for defects is decomposed into “defect OPE blocks”, the irreducible representations of the conformal group, each of which packages the contribution from a primary operator and its d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP01(2018)013 |
| _version_ | 1818545649114677248 |
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| author | Masayuki Fukuda Nozomu Kobayashi Tatsuma Nishioka |
| author_facet | Masayuki Fukuda Nozomu Kobayashi Tatsuma Nishioka |
| author_sort | Masayuki Fukuda |
| collection | DOAJ |
| description | Abstract We study the operator product expansion (OPE) for scalar conformal defects of any codimension in CFT. The OPE for defects is decomposed into “defect OPE blocks”, the irreducible representations of the conformal group, each of which packages the contribution from a primary operator and its descendants. We use the shadow formalism to deduce an integral representation of the defect OPE blocks. They are shown to obey a set of constraint equations that can be regarded as equations of motion for a scalar field propagating on the moduli space of the defects. By employing the Radon transform between the AdS space and the moduli space, we obtain a formula of constructing an AdS scalar field from the defect OPE block for a conformal defect of any codimension in a scalar representation of the conformal group, which turns out to be the Euclidean version of the HKLL formula. We also introduce a duality between conformal defects of different codimensions and prove the equivalence between the defect OPE block for codimension-two defects and the OPE block for a pair of local operators. |
| first_indexed | 2024-12-12T07:42:50Z |
| format | Article |
| id | doaj.art-0d5eba5857444361936156b811750be3 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-12T07:42:50Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0d5eba5857444361936156b811750be32022-12-22T00:32:43ZengSpringerOpenJournal of High Energy Physics1029-84792018-01-012018114710.1007/JHEP01(2018)013Operator product expansion for conformal defectsMasayuki Fukuda0Nozomu Kobayashi1Tatsuma Nishioka2Department of Physics, Faculty of Science, The University of TokyoDepartment of Physics, Faculty of Science, The University of TokyoDepartment of Physics, Faculty of Science, The University of TokyoAbstract We study the operator product expansion (OPE) for scalar conformal defects of any codimension in CFT. The OPE for defects is decomposed into “defect OPE blocks”, the irreducible representations of the conformal group, each of which packages the contribution from a primary operator and its descendants. We use the shadow formalism to deduce an integral representation of the defect OPE blocks. They are shown to obey a set of constraint equations that can be regarded as equations of motion for a scalar field propagating on the moduli space of the defects. By employing the Radon transform between the AdS space and the moduli space, we obtain a formula of constructing an AdS scalar field from the defect OPE block for a conformal defect of any codimension in a scalar representation of the conformal group, which turns out to be the Euclidean version of the HKLL formula. We also introduce a duality between conformal defects of different codimensions and prove the equivalence between the defect OPE block for codimension-two defects and the OPE block for a pair of local operators.http://link.springer.com/article/10.1007/JHEP01(2018)013AdS-CFT CorrespondenceConformal Field Theory |
| spellingShingle | Masayuki Fukuda Nozomu Kobayashi Tatsuma Nishioka Operator product expansion for conformal defects Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory |
| title | Operator product expansion for conformal defects |
| title_full | Operator product expansion for conformal defects |
| title_fullStr | Operator product expansion for conformal defects |
| title_full_unstemmed | Operator product expansion for conformal defects |
| title_short | Operator product expansion for conformal defects |
| title_sort | operator product expansion for conformal defects |
| topic | AdS-CFT Correspondence Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP01(2018)013 |
| work_keys_str_mv | AT masayukifukuda operatorproductexpansionforconformaldefects AT nozomukobayashi operatorproductexpansionforconformaldefects AT tatsumanishioka operatorproductexpansionforconformaldefects |