Path integral quantization of null bosonic strings with Carroll-Weyl ghosts

Sarthak Duary; Sourav Maji

arxiv: 2606.04999 · v2 · pith:MUN5TZKFnew · submitted 2026-06-03 · ✦ hep-th

Path integral quantization of null bosonic strings with Carroll-Weyl ghosts

Sarthak Duary , Sourav Maji This is my paper

Pith reviewed 2026-06-28 05:29 UTC · model grok-4.3

classification ✦ hep-th

keywords null bosonic stringsCarrollian worldsheetpath integral quantizationBMS ghostsCarroll-Weyl scalingBRST complexconformal anomalygauge fixing

0 comments

The pith

Null bosonic string path integrals require an extra scalar ghost pair to fix Carroll-Weyl scaling on the Carrollian worldsheet.

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

The paper claims that the standard BMS bc ghost system used for null strings leaves the Carroll-Weyl scaling symmetry unfixed. This scaling is generated by the Hamiltonian C3 = P·X and must be gauge-fixed like Diff × Weyl before the quantum theory is defined. Adding the corresponding Faddeev-Popov determinant produces a bcs ghost system whose action, residual symmetries, and BRST complex differ from the BMS case alone. The usual check that the anomaly vanishes at D=26 therefore applies only to a partially gauge-fixed theory; the Carroll-Weyl covariant version must include the new s, b^s sector. A reader cares because the consistency condition for the quantum null string changes once every local gauge symmetry is accounted for.

Core claim

The correct ghost system is a bcs system: the BMS bc ghosts plus a scalar ghost s and scalar antighost b^s for Carroll-Weyl scaling. The paper derives the revised path integral, the bcs-ghost action, its residual symmetry equations, mode expansion, and its relation to the extended BMS algebra. This changes the BRST complex and the anomaly problem, so the usual D=26 check based only on the old BMS bc ghosts is a partially gauge-fixed calculation.

What carries the argument

The bcs ghost system obtained by adding the Faddeev-Popov row for the volume-preserving Carroll-Weyl scaling generated by C3 = P·X to the BMS bc system.

If this is right

The path integral measure includes the determinant from the Carroll-Weyl scaling in addition to the BMS bc determinant.
The ghost action contains kinetic terms for the new scalar pair s and b^s.
Residual symmetry equations and mode expansions receive contributions from the s, b^s sector.
The BRST cohomology and anomaly cancellation condition must be re-evaluated with the enlarged ghost content.
Any relation of the ghost system to the extended BMS algebra incorporates the new generators associated with Carroll-Weyl scaling.

Where Pith is reading between the lines

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

The same logic would require additional ghost pairs whenever a Carrollian theory retains an unfixed volume-preserving scaling symmetry.
The shift in anomaly structure may alter which null-string backgrounds admit consistent quantization.
The construction suggests a systematic way to gauge-fix all local Carrollian symmetries order by order in the path integral.

Load-bearing premise

All local gauge symmetries of the Carrollian worldsheet, including the volume-preserving Carroll-Weyl scaling, must be gauge-fixed before the quantum theory is defined.

What would settle it

An explicit computation of the total central charge or conformal anomaly in the full bcs ghost system that yields a different critical dimension from the BMS-bc-only result.

read the original abstract

We revisit the path integral quantization of the null bosonic string from the viewpoint that all local gauge symmetries of the Carrollian worldsheet must be gauge fixed before the quantum theory is defined. In the tensile-string construction the $bc$ ghosts are the Faddeev-Popov determinant for fixing $\mathrm{Diff}\times\mathrm{Weyl}$. In the ILST null string this logic gives the BMS $bc$ system. However, a Carrollian worldsheet admits an additional volume-preserving Carroll-Weyl scaling, whose Hamiltonian generator is $C_3=P\cdot X$. Keeping this scaling as a genuine local gauge symmetry adds one more Faddeev-Popov row. The correct ghost system is therefore a $bcs$ system: the BMS $bc$ ghosts plus a scalar ghost $s$ and scalar antighost $b^s$ for Carroll-Weyl scaling. We derive the revised path integral, the $bcs$-ghost action, its residual symmetry equations, mode expansion, and its relation to the extended BMS algebra. The result changes the BRST complex and the anomaly problem: the usual $D=26$ check based only on the old BMS $bc$ ghosts is a partially gauge-fixed calculation, while the Carroll-Weyl covariant quantum theory must include the $s,b^s$ sector.

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.

Desk Editor's Note private letter to a colleague

The paper adds a scalar ghost pair for Carroll-Weyl scaling on top of the BMS bc system, but the independence of that scaling from existing BMS gauge orbits still needs an explicit check.

read the letter

The core claim is that the null bosonic string on a Carrollian worldsheet has one more local gauge symmetry than the ILST treatment accounted for. The volume-preserving Carroll-Weyl scaling generated by C3 = P·X is treated as independent, so the Faddeev-Popov determinant gains an extra scalar pair s and b^s. This produces a bcs ghost system whose action, residual symmetries, and mode expansion are worked out, and it alters the BRST complex and the anomaly calculation. The usual D=26 check is therefore described as only partially gauge-fixed.

The paper does the straightforward thing: it applies the same path-integral logic used for Diff × Weyl in the tensile case and for BMS in the null case, now including the extra scaling. The derivation of the ghost action and its relation to the extended BMS algebra follows directly from that choice. That is the actual technical increment.

The soft spot is the assumption that the new symmetry is independent enough to require its own FP row. The abstract adopts the viewpoint that all local symmetries must be fixed, but does not show in the provided text that the gauge transformations generated by C3 lie outside the BMS orbit or that the combined Jacobian factors cleanly. If the full manuscript contains an explicit algebra closure check or a concrete gauge-fixing condition that demonstrates the extra determinant is non-redundant, the concern disappears; otherwise the bcs construction risks being an overcount. The anomaly shift and the revised D=26 statement rest on this point.

The work is aimed at the small group already using BMS ghosts for tensionless or Carrollian strings. A reader who already knows the bc system will see the extension immediately and can judge whether the extra pair changes their calculations. It is narrow but internally consistent on its own terms.

I would send it to peer review. The logic is clear, the subfield is specialized, and a referee can check the algebra and the Jacobian in one pass.

Referee Report

1 major / 0 minor

Summary. The manuscript argues that the path integral quantization of the null bosonic string on a Carrollian worldsheet requires gauge-fixing all local symmetries, including an additional volume-preserving Carroll-Weyl scaling generated by C3 = P·X. This necessitates extending the standard BMS bc ghost system by one more Faddeev-Popov row, yielding a bcs ghost system with an extra scalar ghost s and antighost b^s. The paper derives the revised path integral, bcs-ghost action, residual symmetries, mode expansions, and their relation to the extended BMS algebra, concluding that the usual D=26 anomaly check is only a partially gauge-fixed calculation.

Significance. If the central claim holds, the result would revise the quantization of null strings by showing that prior treatments have not fully accounted for Carrollian symmetries, altering the BRST complex and anomaly cancellation. This could have implications for the consistency of the quantum theory and its connection to extended BMS structures. The derivations of the bcs action and mode expansions would provide concrete tools for further study if the independence of the symmetries is rigorously established.

major comments (1)

The central claim that the Carroll-Weyl scaling is an independent local gauge symmetry whose Faddeev-Popov determinant adds a distinct scalar pair (s, b^s) on top of the BMS bc system is load-bearing for the conclusion that the D=26 check is partially gauge-fixed. The abstract adopts this as the viewpoint but supplies no explicit check of the algebra closure between C3 = P·X and the BMS generators or of the factorization of the combined Jacobian, which is required to confirm that the extra row in the FP matrix is non-redundant.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and for identifying the need for explicit verification of the independence of the Carroll-Weyl symmetry. We address the single major comment below.

read point-by-point responses

Referee: The central claim that the Carroll-Weyl scaling is an independent local gauge symmetry whose Faddeev-Popov determinant adds a distinct scalar pair (s, b^s) on top of the BMS bc system is load-bearing for the conclusion that the D=26 check is partially gauge-fixed. The abstract adopts this as the viewpoint but supplies no explicit check of the algebra closure between C3 = P·X and the BMS generators or of the factorization of the combined Jacobian, which is required to confirm that the extra row in the FP matrix is non-redundant.

Authors: We agree that an explicit verification of the Poisson-bracket closure between the Carroll-Weyl generator C3 = P·X and the BMS generators, together with a demonstration that the combined Faddeev-Popov Jacobian factorizes, is required to place the independence of the extra scalar ghost pair on a firm footing. The manuscript motivates the additional symmetry from the geometry of the Carrollian worldsheet, but does not perform these calculations. In the revised version we will add a dedicated appendix that computes the relevant brackets, confirms that C3 does not lie in the BMS algebra, and shows that the full determinant separates into the standard BMS bc factor times a distinct scalar determinant for (s, b^s). This will directly address the concern that the extra FP row might be redundant. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation applies standard FP logic to an adopted gauge-fixing premise

full rationale

The paper states its central premise upfront as an adopted viewpoint ('all local gauge symmetries of the Carrollian worldsheet must be gauge fixed before the quantum theory is defined') and then applies the usual Faddeev-Popov construction to the additional Carroll-Weyl scaling generated by C3 = P·X. No equation or result is shown to reduce by construction to a fitted parameter, a self-definition, or a self-citation chain; the bcs ghost system is derived directly from the extra row in the FP determinant. The manuscript contains no load-bearing self-citations of uniqueness theorems or ansatze from the same authors, and the D=26 anomaly discussion is presented as a consequence of the extended gauge fixing rather than an input. The derivation is therefore self-contained against external benchmarks of path-integral quantization.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the domain assumption that every local Carrollian symmetry must be gauge-fixed before quantization and on the identification of the Carroll-Weyl scaling as an independent local gauge symmetry generated by C3 = P·X; no free parameters or new physical entities beyond standard Faddeev-Popov ghosts are introduced.

axioms (2)

domain assumption All local gauge symmetries of the Carrollian worldsheet must be gauge-fixed before the quantum theory is defined.
Stated as the adopted viewpoint in the first sentence of the abstract.
domain assumption The Carrollian worldsheet admits an additional volume-preserving Carroll-Weyl scaling symmetry whose Hamiltonian generator is C3 = P·X.
Invoked to justify the extra Faddeev-Popov row.

invented entities (1)

scalar ghost s and scalar antighost b^s no independent evidence
purpose: Faddeev-Popov determinant for the Carroll-Weyl scaling symmetry
Introduced as the additional ghost pair required by the extra local symmetry; they are standard auxiliary fields, not new physical particles.

pith-pipeline@v0.9.1-grok · 5768 in / 1677 out tokens · 27137 ms · 2026-06-28T05:29:18.925604+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

The conformal null string in $d+2$ and $d$ dimensions
hep-th 2026-06 unverdicted novelty 3.0

The conformal null string reduces from d+2 to d dimensions via Dirac slices, with the Virasoro-su(1,1) algebra mapping to Carrollian-Weyl symmetry.

Reference graph

Works this paper leans on

23 extracted references · 14 linked inside Pith · cited by 1 Pith paper

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D. J. Gross and P. F. Mende,The high-energy behavior of string scattering amplitudes,Phys. Lett. B197(1987) 129

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1988

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A. Bagchi, S. Chakrabortty and P. Parekh,Tensionless Strings from Worldsheet Symmetries, JHEP01(2016) 158 [1507.04361]

Pith/arXiv arXiv 2016

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Pith/arXiv arXiv 2017

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Pith/arXiv arXiv 2014

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Pith/arXiv arXiv

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Pith/arXiv arXiv

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Pith/arXiv arXiv

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arXiv