Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization
Abstract Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the planar four-point functions at arbitrary ’t Hooft coup...
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doaj-3439ae2df0d94ba39878dc6c6e336a322020-11-25T03:41:08ZengSpringerOpenJournal of High Energy Physics1029-84792020-10-0120201013210.1007/JHEP10(2020)007Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonizationZhijin Li0Centro de Física do Porto, Departamento de Físicae Astronomia, Faculdade de Ciências da Universidade do PortoAbstract Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the planar four-point functions at arbitrary ’t Hooft coupling λ in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the λ expansions of the correlation functions. The λ expansions terminate at order λ 2 and the solutions are exact in λ. Our work generalizes the approach proposed by Maldacena and Zhiboedov to four-point correlators, and it amounts to an on-shell study for the 3D Chern-Simons vector models and their holographic duals in AdS 4. Besides, we show that the same results can also be obtained rather simply from bosonization duality of 3D Chern-Simons vector models. The odd term at order O(λ) in the spinning four-point function relates to the free boson correlator through a Legendre transformation. This provides new evidence on the 3D bosonization duality at the spinning four-point function level. We expect this work can be generalized to a complete classification of general four-point functions of single trace currents.http://link.springer.com/article/10.1007/JHEP10(2020)007Chern-Simons TheoriesDuality in Gauge Field TheoriesHigher Spin Symmetry1/N Expansion |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zhijin Li |
spellingShingle |
Zhijin Li Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization Journal of High Energy Physics Chern-Simons Theories Duality in Gauge Field Theories Higher Spin Symmetry 1/N Expansion |
author_facet |
Zhijin Li |
author_sort |
Zhijin Li |
title |
Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization |
title_short |
Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization |
title_full |
Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization |
title_fullStr |
Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization |
title_full_unstemmed |
Bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3D bosonization |
title_sort |
bootstrapping conformal four-point correlators with slightly broken higher spin symmetry and 3d bosonization |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-10-01 |
description |
Abstract Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the planar four-point functions at arbitrary ’t Hooft coupling λ in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the λ expansions of the correlation functions. The λ expansions terminate at order λ 2 and the solutions are exact in λ. Our work generalizes the approach proposed by Maldacena and Zhiboedov to four-point correlators, and it amounts to an on-shell study for the 3D Chern-Simons vector models and their holographic duals in AdS 4. Besides, we show that the same results can also be obtained rather simply from bosonization duality of 3D Chern-Simons vector models. The odd term at order O(λ) in the spinning four-point function relates to the free boson correlator through a Legendre transformation. This provides new evidence on the 3D bosonization duality at the spinning four-point function level. We expect this work can be generalized to a complete classification of general four-point functions of single trace currents. |
topic |
Chern-Simons Theories Duality in Gauge Field Theories Higher Spin Symmetry 1/N Expansion |
url |
http://link.springer.com/article/10.1007/JHEP10(2020)007 |
work_keys_str_mv |
AT zhijinli bootstrappingconformalfourpointcorrelatorswithslightlybrokenhigherspinsymmetryand3dbosonization |
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