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arxiv: 2606.08387 · v1 · pith:SMTWC3ABnew · submitted 2026-06-07 · ✦ hep-th

Notes on noninvertible quantum symmetries in two dimensions

P. Banerjee , E. Sharpe This is my paper

Pith reviewed 2026-06-27 18:22 UTC · model grok-4.3

classification ✦ hep-th
keywords noninvertible symmetriesRep(G) symmetriesorbifoldspartition functionstwo-dimensional theoriesgaugingquantum symmetries
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The pith

Partition functions of Rep(G)-gauged nonabelian G orbifolds match the original theories.

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

The paper presents a systematic procedure to calculate partition functions when noninvertible Rep(G) quantum symmetries act on two-dimensional nonabelian G orbifolds. It applies the method to multiplicity-free cases for several nonabelian groups. The calculations confirm that gauging an orbifold with Rep(G) yields the same partition function as the starting theory. This step makes the action of such symmetries concrete in explicit models where general principles already predict the match.

Core claim

A systematic procedure computes partition functions of noninvertible Rep(G) quantum symmetry actions on two-dimensional nonabelian G orbifolds. In multiplicity-free examples for several nonabelian groups, the partition function of the Rep(G)-gauged G orbifold equals that of the original theory.

What carries the argument

A systematic procedure for computing partition functions of noninvertible Rep(G) symmetry actions on nonabelian orbifolds.

If this is right

  • The equivalence of partition functions holds explicitly for the tested nonabelian groups.
  • Noninvertible symmetries can be realized through concrete operations on orbifold partition functions.
  • Gauging with Rep(G) leaves the partition function invariant as required by general principles.
  • The procedure fills a gap by providing explicit checks for nonabelian cases.

Where Pith is reading between the lines

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

  • The method might apply to orbifolds with multiplicities or to other classes of noninvertible symmetries.
  • Similar procedures could test invariance under related gaugings in two-dimensional theories.
  • Explicit examples may help classify which noninvertible symmetries preserve partition functions.

Load-bearing premise

The systematic procedure correctly implements the action of the noninvertible Rep(G) quantum symmetries on the nonabelian G orbifolds in the multiplicity-free examples considered.

What would settle it

Explicit computation of the partition function for a nonabelian group such as S3 via the procedure, followed by a mismatch with the original theory's partition function.

read the original abstract

In this note we describe a systematic procedure for computing partition functions of noninvertible Rep ($G$) quantum symmetry actions on two-dimensional nonabelian $G$ orbifolds. We apply this procedure to multiplicity-free examples for several nonabelian groups, and check explicitly in those examples that the partition function of a two-dimensional Rep ($G$)-gauged $G$ orbifold, for nonabelian $G$, matches that of the original theory, as expected on general principles. This fills a minor gap in the literature, making quantum symmetries in two-dimensional nonabelian orbifolds more concrete.

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

0 major / 0 minor

Summary. The paper presents a systematic procedure for computing partition functions of noninvertible Rep(G) quantum symmetry actions on two-dimensional nonabelian G orbifolds. It applies the procedure to multiplicity-free examples for several nonabelian groups and explicitly verifies that the partition function of the Rep(G)-gauged G orbifold matches that of the original theory, consistent with expectations from general principles. This is positioned as filling a minor gap by making the construction concrete.

Significance. If the explicit checks hold, the work provides useful concrete realizations of noninvertible symmetries in nonabelian orbifolds, aiding further study in 2d CFTs. The verification against independently expected results strengthens the procedure without introducing new claims beyond the literature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive recommendation to accept. The report accurately summarizes the scope and contribution of the work.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central contribution is an explicit computational procedure applied to multiplicity-free examples, followed by verification that the resulting partition functions match an independently expected equality (gauged Rep(G) orbifold equals original theory) on general principles. This verification is presented as confirmation rather than a fit or derivation; no load-bearing step reduces by construction to the paper's own inputs, fitted parameters, or self-citation chains. The work is self-contained against external benchmarks and fills a gap by making known expectations concrete.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no information on free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5617 in / 1014 out tokens · 25660 ms · 2026-06-27T18:22:50.832940+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

9 extracted references · 2 linked inside Pith

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