SciPost Submission Page
Higher-form anomalies and state-operator correspondence beyond conformal invariance
by Stathis Vitouladitis
Submission summary
| Authors (as registered SciPost users): | Stathis Vitouladitis |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00060v2 (pdf) |
| Date submitted: | Nov. 20, 2025, 11:35 p.m. |
| Submitted by: | Stathis Vitouladitis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
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- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
- Added a sentence below eq. (1.2) to define $ \widetilde{Q}_n $. Added missing tilde in eq. (1.3).
- Added reference [45] at line 171, following an external suggestion.
- Expanded footnote 6, regarding higher-derivative corrections.
- Added definition of $ d^\dagger $ below eq. (2.15).
- Added a sentence to explain gauge redundancy near line 251.
- Added a clarification in line 312.
- Added footnote 10 to address the conformal coupling in curved spacetime; added reference [62] in the main text around that point.
- Clarified the dependence of the symmetry algebra on the spatial manifold in line 378.
- Corrected the characterisation of $ \left|\theta\right> $ above eq. (3.23).
- Removed the inaccurate mention of disorder operators below (3.30).
- Added an explanation of the squeezing operator in line 611.
- Added a clarifying sentence in line 672.
- Corrected the requirement of eq. (5.4) right above this equation.