Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges, by António Antunes, Nat Levine, Marco Meineri

SciPost Physics Home Authoring Refereeing Submit a manuscript About Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges António Antunes, Nat Levine, Marco Meineri SciPost Phys. 20, 088 (2026) · published 23 March 2026 doi: 10.21468/SciPostPhys.20.3.088 pdf BiBTeX RIS Submissions/Reports Abstract Higher-spin conserved currents and charges feature prominently in integrable 2d QFTs in flat space. Motivated by the question of integrable field theories in AdS space, we consider the consequences of higher-spin currents for QFTs in AdS$_2$, and find that their effect is much more constraining than in flat space. Specifically, it is impossible to preserve: (a) any higher-spin charges when deforming a free field of generic mass by interactions (even boundary-localized), or (b) any spin-4 charges when deforming a CFT by a Virasoro primary. Therefore, in these settings, there are no integrable theories in AdS with higher-spin conserved charges. Along the way, we explain how higher-spin charges lead to integer spacing in the spectrum of primaries, sum rules on the OPE data, and constraints on correlation functions. We also explain a key difference between AdS and flat space: in AdS one cannot 'partially' conserve a higher-spin current along particular directions, since the AdS isometries imply full conservation. Finally, we describe the consequences of higher-spin symmetry breaking on the spectrum of long-range models. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.3.088TI - Demystifying integrable QFTs in AdS: No-go theorems for higher-spin chargesPY - 2026/03/23UR - https://scipost.org/SciPostPhys.20.3.088JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 3SP - 088A1 - Antunes, AntónioAU - Levine, NatAU - Meineri, MarcoAB - Higher-spin conserved currents and charges feature prominently in integrable 2d QFTs in flat space. Motivated by the question of integrable field theories in AdS space, we consider the consequences of higher-spin currents for QFTs in AdS$_2$, and find that their effect is much more constraining than in flat space. Specifically, it is impossible to preserve: (a) any higher-spin charges when deforming a free field of generic mass by interactions (even boundary-localized), or (b) any spin-4 charges when deforming a CFT by a Virasoro primary. Therefore, in these settings, there are no integrable theories in AdS with higher-spin conserved charges. Along the way, we explain how higher-spin charges lead to integer spacing in the spectrum of primaries, sum rules on the OPE data, and constraints on correlation functions. We also explain a key difference between AdS and flat space: in AdS one cannot 'partially' conserve a higher-spin current along particular directions, since the AdS isometries imply full conservation. Finally, we describe the consequences of higher-spin symmetry breaking on the spectrum of long-range models.ER - × @Article{10.21468/SciPostPhys.20.3.088, title={{Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges}}, author={António Antunes and Nat Levine and Marco Meineri}, journal={SciPost Phys.}, volume={20}, pages={088}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.3.088}, url={https://scipost.org/10.21468/SciPostPhys.20.3.088},} Ontology / Topics See full Ontology or Topics database. Anti-de Sitter (AdS) space Conformal field theory (CFT) Integrability/integrable models Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 3 4 5 António Antunes, 2 3 4 5 6 Nat Levine, 7 8 Marco Meineri 1 Deutsches Elektronen-Synchrotron / Deutsche Elektronen-Synchrotron DESY [DESY] 2 Sorbonne Université / Sorbonne University 3 Université de Paris / University of Paris 4 Laboratoire de Physique de l’École Normale Supérieure / Physics Laboratory of the École Normale Supérieure [LPENS] 5 Université de recherche Paris Sciences et Lettres / PSL Research University [PSL] 6 Institute for Theoretical Physics Amsterdam [ITFA] 7 Università degli Studi di Torino / University of Turin [UNITO] 8 Istituto Nazionale di Fisica Nucleare Sezione di Torino / INFN Sezione di Torino Funders for the research work leading to this publication Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG] European Research Council [ERC] FP7 Seventh Framework Programme (FP7) (through Organization: European Commission [EC]) Ministero dell'Università e della Ricerca Universiteit van Amsterdam / University of Amsterdam [UvA] École Normale Supérieure [ENS]