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...
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Autor*in:	Masayuki Fukuda [verfasserIn] Nozomu Kobayashi [verfasserIn] Tatsuma Nishioka [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	AdS-CFT Correspondence Conformal Field Theory

Übergeordnetes Werk:	In: Journal of High Energy Physics - SpringerOpen, 2016, (2018), 1, Seite 47
Übergeordnetes Werk:	year:2018 ; number:1 ; pages:47

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1007/JHEP01(2018)013

Katalog-ID:	DOAJ042412404

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520			\|a 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.
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allfields	10.1007/JHEP01(2018)013 doi (DE-627)DOAJ042412404 (DE-599)DOAJ0d5eba5857444361936156b811750be3 DE-627 ger DE-627 rakwb eng QC770-798 Masayuki Fukuda verfasserin aut Operator product expansion for conformal defects 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. AdS-CFT Correspondence Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity Nozomu Kobayashi verfasserin aut Tatsuma Nishioka verfasserin aut In Journal of High Energy Physics SpringerOpen, 2016 (2018), 1, Seite 47 (DE-627)320910571 (DE-600)2027350-2 10298479 nnns year:2018 number:1 pages:47 https://doi.org/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/article/0d5eba5857444361936156b811750be3 kostenfrei http://link.springer.com/article/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/toc/1029-8479 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 47
spelling	10.1007/JHEP01(2018)013 doi (DE-627)DOAJ042412404 (DE-599)DOAJ0d5eba5857444361936156b811750be3 DE-627 ger DE-627 rakwb eng QC770-798 Masayuki Fukuda verfasserin aut Operator product expansion for conformal defects 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. AdS-CFT Correspondence Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity Nozomu Kobayashi verfasserin aut Tatsuma Nishioka verfasserin aut In Journal of High Energy Physics SpringerOpen, 2016 (2018), 1, Seite 47 (DE-627)320910571 (DE-600)2027350-2 10298479 nnns year:2018 number:1 pages:47 https://doi.org/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/article/0d5eba5857444361936156b811750be3 kostenfrei http://link.springer.com/article/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/toc/1029-8479 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 47
allfields_unstemmed	10.1007/JHEP01(2018)013 doi (DE-627)DOAJ042412404 (DE-599)DOAJ0d5eba5857444361936156b811750be3 DE-627 ger DE-627 rakwb eng QC770-798 Masayuki Fukuda verfasserin aut Operator product expansion for conformal defects 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. AdS-CFT Correspondence Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity Nozomu Kobayashi verfasserin aut Tatsuma Nishioka verfasserin aut In Journal of High Energy Physics SpringerOpen, 2016 (2018), 1, Seite 47 (DE-627)320910571 (DE-600)2027350-2 10298479 nnns year:2018 number:1 pages:47 https://doi.org/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/article/0d5eba5857444361936156b811750be3 kostenfrei http://link.springer.com/article/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/toc/1029-8479 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 47
allfieldsGer	10.1007/JHEP01(2018)013 doi (DE-627)DOAJ042412404 (DE-599)DOAJ0d5eba5857444361936156b811750be3 DE-627 ger DE-627 rakwb eng QC770-798 Masayuki Fukuda verfasserin aut Operator product expansion for conformal defects 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. AdS-CFT Correspondence Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity Nozomu Kobayashi verfasserin aut Tatsuma Nishioka verfasserin aut In Journal of High Energy Physics SpringerOpen, 2016 (2018), 1, Seite 47 (DE-627)320910571 (DE-600)2027350-2 10298479 nnns year:2018 number:1 pages:47 https://doi.org/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/article/0d5eba5857444361936156b811750be3 kostenfrei http://link.springer.com/article/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/toc/1029-8479 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 47
allfieldsSound	10.1007/JHEP01(2018)013 doi (DE-627)DOAJ042412404 (DE-599)DOAJ0d5eba5857444361936156b811750be3 DE-627 ger DE-627 rakwb eng QC770-798 Masayuki Fukuda verfasserin aut Operator product expansion for conformal defects 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. AdS-CFT Correspondence Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity Nozomu Kobayashi verfasserin aut Tatsuma Nishioka verfasserin aut In Journal of High Energy Physics SpringerOpen, 2016 (2018), 1, Seite 47 (DE-627)320910571 (DE-600)2027350-2 10298479 nnns year:2018 number:1 pages:47 https://doi.org/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/article/0d5eba5857444361936156b811750be3 kostenfrei http://link.springer.com/article/10.1007/JHEP01(2018)013 kostenfrei https://doaj.org/toc/1029-8479 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2018 1 47
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callnumber-first	Q - Science
author	Masayuki Fukuda
spellingShingle	Masayuki Fukuda misc QC770-798 misc AdS-CFT Correspondence misc Conformal Field Theory misc Nuclear and particle physics. Atomic energy. Radioactivity Operator product expansion for conformal defects
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topic_title	QC770-798 Operator product expansion for conformal defects AdS-CFT Correspondence Conformal Field Theory
topic	misc QC770-798 misc AdS-CFT Correspondence misc Conformal Field Theory misc Nuclear and particle physics. Atomic energy. Radioactivity
topic_unstemmed	misc QC770-798 misc AdS-CFT Correspondence misc Conformal Field Theory misc Nuclear and particle physics. Atomic energy. Radioactivity
topic_browse	misc QC770-798 misc AdS-CFT Correspondence misc Conformal Field Theory misc Nuclear and particle physics. Atomic energy. Radioactivity
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title	Operator product expansion for conformal defects
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title_full	Operator product expansion for conformal defects
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title_sort	operator product expansion for conformal defects
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title_auth	Operator product expansion for conformal defects
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	Operator product expansion for conformal defects
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