Higher-form anomalies and state-operator correspondence beyond conformal invariance, by Stathis Vitouladitis

SciPost Physics Home Authoring Refereeing Submit a manuscript About Higher-form anomalies and state-operator correspondence beyond conformal invariance Stathis Vitouladitis SciPost Phys. 20, 011 (2026) · published 19 January 2026 doi: 10.21468/SciPostPhys.20.1.011 pdf BiBTeX RIS Submissions/Reports Abstract We establish a state-operator correspondence for a class of non-conformal quantum field theories with continuous higher-form symmetries and a mixed anomaly. Such systems can always be realised as a relativistic superfluid. The symmetry structure induces an infinite tower of conserved charges, which we construct explicitly. These charges satisfy an abelian current algebra with a central extension, generalising the familiar Kac–Moody algebras to higher dimensions. States and operators are organised into representations of this algebra, enabling a direct correspondence. We demonstrate the correspondence explicitly in free examples by performing the Euclidean path integral on a $d$-dimensional ball, with local operators inserted in the origin, and matching to energy eigenstates on $S^{d-1}$ obtained by canonical quantisation. Interestingly, in the absence of conformal invariance, the empty path integral prepares a squeezed vacuum rather than the true ground state. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.011TI - Higher-form anomalies and state-operator correspondence beyond conformal invariancePY - 2026/01/19UR - https://scipost.org/SciPostPhys.20.1.011JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 011A1 - Vitouladitis, StathisAB - We establish a state-operator correspondence for a class of non-conformal quantum field theories with continuous higher-form symmetries and a mixed anomaly. Such systems can always be realised as a relativistic superfluid. The symmetry structure induces an infinite tower of conserved charges, which we construct explicitly. These charges satisfy an abelian current algebra with a central extension, generalising the familiar Kac–Moody algebras to higher dimensions. States and operators are organised into representations of this algebra, enabling a direct correspondence. We demonstrate the correspondence explicitly in free examples by performing the Euclidean path integral on a $d$-dimensional ball, with local operators inserted in the origin, and matching to energy eigenstates on $S^{d-1}$ obtained by canonical quantisation. Interestingly, in the absence of conformal invariance, the empty path integral prepares a squeezed vacuum rather than the true ground state.ER - × @Article{10.21468/SciPostPhys.20.1.011, title={{Higher-form anomalies and state-operator correspondence beyond conformal invariance}}, author={Stathis Vitouladitis}, journal={SciPost Phys.}, volume={20}, pages={011}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.011}, url={https://scipost.org/10.21468/SciPostPhys.20.1.011},} Ontology / Topics See full Ontology or Topics database. 't Hooft anomalies Abelian symmetries Conserved charges Global symmetries Quantum field theory (QFT) Superfluidity Author / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Stathis Vitouladitis 1 Université Libre de Bruxelles [ULB] 2 International Solvay Institutes Funders for the research work leading to this publication Fonds De La Recherche Scientifique - FNRS (FNRS) (through Organization: Fonds National de la Recherche Scientifique [FNRS]) Solvay