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arxiv: 2511.11343 · v2 · pith:OEV7KT4Cnew · submitted 2025-11-14 · ✦ hep-th · cond-mat.str-el

Global symmetries: locality, unitarity, and regularity

Ibrahima Bah , Shlomo S. Razamat , Michal Shemesh , Hannah Tillim This is my paper

Pith reviewed 2026-05-21 18:21 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords global symmetriescategorical symmetriesnon-invertible symmetrieslocalityunitarityHilbert spacefusion algebraquantum field theory
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The pith

Locality imposes regularities on how symmetries act on the Hilbert space, enabling an observable that encodes fusion algebra data for non-invertible symmetries.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the tension between locality and unitarity in quantum field theories that possess categorical symmetries, where symmetry operators are typically non-invertible. It argues that locality nonetheless forces specific regular patterns in the way these operators act on the Hilbert space. These patterns make it possible to define a new observable that quantifies aspects of non-locality for the symmetry operators. The authors test the observable on a class of examples and show that its values capture information from the fusion algebra of the symmetries. A sympathetic reader would care because the construction offers a concrete diagnostic for how locality and unitarity constrain generalized symmetries without requiring invertibility.

Core claim

Locality imposes particular regularities in the action of symmetries on the Hilbert space. This allows introduction of an observable that measures properties of the non-locality for symmetry operators and encodes data associated to the fusion algebra of symmetries.

What carries the argument

An observable that quantifies non-locality properties of symmetry operators by exploiting locality-imposed regularities on their Hilbert-space action.

If this is right

  • The observable supplies a practical diagnostic for non-locality of symmetry operators without assuming invertibility.
  • Fusion-algebra data can be extracted from Hilbert-space regularities in models with categorical symmetries.
  • The construction applies to a range of examples in quantum field theory where non-invertible symmetries appear.
  • Unitarity and locality remain compatible once the regularities in symmetry actions are properly accounted for.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same regularity-based observable might be computed in lattice models or holographic setups to test consistency with continuum fusion rules.
  • If the observable proves robust, it could serve as a tool to classify or constrain possible fusion algebras in theories where direct operator fusion is hard to access.
  • The approach may extend to time-dependent or thermal states, revealing how locality regularities evolve with temperature or time.

Load-bearing premise

The regularities imposed by locality on the Hilbert-space action are sufficiently strong and universal to define an observable whose measured values reliably encode fusion-algebra data across the studied class of examples.

What would settle it

Explicit computation of the observable in one of the paper's example models where the fusion algebra is independently known; if the observable fails to reproduce the expected fusion coefficients or shows inconsistent scaling with system size, the claimed encoding would be refuted.

read the original abstract

We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality imposes particular regularities in the action of symmetries on the Hilbert space. This allows us to introduce an observable that can measure the properties of the non-locality for symmetry operators. We study it for a class of examples and demonstrate that this observable can encode data associated to the fusion algebra of symmetries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript studies the tension between locality and unitarity for categorical (generically non-invertible) symmetries in quantum field theory. It argues that locality imposes regularities on the action of symmetry operators on the Hilbert space, which permits the introduction of an observable measuring properties of non-locality for these operators. The observable is studied in a class of examples, where it is shown to encode data associated to the fusion algebra of the symmetries.

Significance. If the central claim holds, the work would supply a concrete link between locality constraints and fusion data for non-invertible symmetries, potentially yielding a new observable for extracting algebraic information from Hilbert-space actions. The approach is interesting for models where direct fusion-rule computations are difficult, but its broader impact depends on establishing the result beyond the studied examples.

major comments (1)
  1. [Abstract] Abstract: the claim that locality imposes regularities strong enough to define an observable whose values encode fusion-algebra data is presented as following from the locality-unitarity tension, yet the text supplies no general derivation, explicit operator-algebra constraints, or representation-theoretic characterization of these regularities. Without this step, it remains unclear whether agreement in the examples is forced by the stated principles or arises from model-specific choices.
minor comments (2)
  1. The definition and construction of the observable should be stated formally (with explicit dependence on the symmetry operators and Hilbert-space action) before the example studies, to make the subsequent claims easier to follow.
  2. A brief discussion of possible counter-examples or edge cases (e.g., invertible symmetries or theories without a clear notion of non-locality) would help delineate the scope of the result.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The comment raises an important point about the scope of our claims, which we address below by clarifying the presentation and revising the abstract accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that locality imposes regularities strong enough to define an observable whose values encode fusion-algebra data is presented as following from the locality-unitarity tension, yet the text supplies no general derivation, explicit operator-algebra constraints, or representation-theoretic characterization of these regularities. Without this step, it remains unclear whether agreement in the examples is forced by the stated principles or arises from model-specific choices.

    Authors: We agree that the manuscript motivates the regularities from the general tension between locality and unitarity for categorical symmetries but does not supply a universal derivation, explicit operator-algebra constraints, or representation-theoretic characterization that would hold beyond the examples. The argument proceeds by identifying regularities in the Hilbert-space action that follow from locality requirements, which then permit definition of the observable; this is then verified to encode fusion data in the concrete class of models studied. We acknowledge that this leaves open whether the encoding is forced by the principles in full generality or is tied to the model choices. To address the concern, we will revise the abstract to state that the observable encodes fusion-algebra data in the studied examples, and we will add a brief discussion clarifying the example-based nature of the results together with an outline of steps toward a more general treatment. revision: partial

Circularity Check

0 steps flagged

No circularity: observable defined from locality regularities and verified on examples without definitional reduction or self-citation load-bearing

full rationale

The paper argues that locality imposes regularities on the Hilbert-space action of symmetry operators, introduces an observable to measure non-locality properties, and demonstrates in a class of examples that the observable encodes fusion-algebra data. No step reduces by construction to its own inputs: the regularities are asserted as a consequence of locality-unitarity tension rather than defined in terms of the target fusion data, the observable is introduced as a new measurement tool rather than fitted to the fusion rules, and the demonstration is presented as example-based verification rather than a uniqueness theorem or self-citation chain. The derivation remains self-contained against external benchmarks of locality and unitarity constraints, with no quoted equation or premise that equates the observable's output to the fusion algebra by fiat.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim rests on an unstated assumption that locality-regularity relations exist and are measurable.

pith-pipeline@v0.9.0 · 5611 in / 1037 out tokens · 49252 ms · 2026-05-21T18:21:06.571546+00:00 · methodology

discussion (0)

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