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arxiv: 2606.26623 · v1 · pith:KJHOUKF5new · submitted 2026-06-25 · ✦ hep-th · cond-mat.str-el

Central charges C_J and C_T in QED_d-GNY model and scalar QED_d

Yongwei Guo , Zhijin Li This is my paper

Pith reviewed 2026-06-26 03:28 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords central chargesQED-GNY modellarge N expansiondeconfined quantum critical pointtopological symmetrygauge theoryconformal field theory1/N corrections
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The pith

The large-N limit of the QED3-GNY model yields central charges in agreement with those of the SO(5) deconfined quantum critical point.

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

This paper computes the leading 1/N corrections to the central charges C_J and C_T in the QEDd-GNY model and scalar QEDd for general d. In three dimensions it additionally determines the central charge of the topological U(1) symmetry current to the same order. These large-N results for the QED3-GNY model are then compared to nonperturbative data for the SO(5) symmetric deconfined quantum critical point and show reasonable agreement.

Core claim

The leading-order 1/N corrections to the central charges C_J and C_T are obtained in the conformal QEDd-Gross-Neveu-Yukawa model and the scalar QEDd in d dimensions. The scaling dimensions of the lowest adjoint bilinear scalars are also found to O(1/N) for general d. In d=3 the central charge C_J^top of the topological symmetry current is evaluated to subleading order in 1/N. The large N predictions of the QED3-GNY model are found to be in reasonable agreement with the nonperturbative estimates for the SO(5) DQCP.

What carries the argument

The 1/N expansion applied to central charges in the QEDd-GNY model

Load-bearing premise

The QED3-GNY model in the large-N limit provides a faithful description of the SO(5) symmetric deconfined quantum critical point whose central charges can be directly compared to bootstrap and fuzzy-sphere data.

What would settle it

A precise nonperturbative computation of C_J or C_T for the SO(5) deconfined quantum critical point that falls outside the range given by the large-N prediction and its uncertainty.

read the original abstract

We compute the leading-order $1/N$ corrections to the central charges $C_J$ and $C_T$ in the conformal QED$_d$-Gross-Neveu-Yukawa (GNY) model and the scalar QED$_d$ in $d$ dimensions. The scaling dimensions of the lowest adjoint bilinear scalars are obtained to order $O(1/N)$ for general $d$. In $d=3$, the $U(1)$ Abelian gauge theory possesses a topological $U(1)$ global symmetry, and we evaluate the central charge $C_J^{\text{top}}$ of the topological symmetry current to subleading order in the $1/N$ expansion. Our interest in these theories is primarily motivated by their potential connection to the $SO(5)$ symmetric deconfined quantum critical point (DQCP). We compare the large $N$ results for the central charges $C_J$ and $C_T$ with the conformal data of the $SO(5)$ DQCP obtained from fuzzy sphere and conformal bootstrap. The large $N$ predictions of the QED$_3$-GNY model are found to be in reasonable agreement with the nonperturbative estimates for the $SO(5)$ DQCP.

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

2 major / 2 minor

Summary. The manuscript computes the leading 1/N corrections to the central charges C_J and C_T in the conformal QED_d-GNY model and scalar QED_d for general d. It obtains the scaling dimensions of the lowest adjoint bilinear scalars to O(1/N). In d=3 it evaluates the topological central charge C_J^top of the U(1) symmetry current to subleading order in 1/N. The large-N results for C_J and C_T in the QED_3-GNY model are compared to conformal data for the SO(5) DQCP obtained from fuzzy-sphere and bootstrap methods, with the abstract stating that the predictions are in reasonable agreement.

Significance. If the 1/N results are under control and the QED_3-GNY model at large N provides a faithful proxy for the SO(5) DQCP, the explicit expressions for C_J, C_T and the bilinear dimensions supply useful benchmarks that can be tested against future non-perturbative calculations. The subleading computation of the topological C_J^top is a technical advance within the large-N framework.

major comments (2)
  1. [Abstract] Abstract: the claim that the large-N predictions are in 'reasonable agreement' with SO(5) DQCP data rests on the assumption that the QED_3-GNY model at large N faithfully describes the physically relevant small-N regime (N=2 for minimal SO(5)). No estimate of the magnitude of O(1/N^2) corrections or convergence test at N=2 is supplied, so the strength of the comparison cannot be assessed from the given information.
  2. [Abstract] The topological C_J^top is computed only to subleading order at large N, yet the DQCP comparison involves finite-N physics; without a discussion of how higher-order 1/N terms affect the topological contribution when N is lowered, the agreement statement for C_J remains incomplete.
minor comments (2)
  1. The range of d for which the O(1/N) expressions remain valid should be stated explicitly near the first appearance of the central-charge formulas.
  2. Notation for the adjoint bilinear scalars and the distinction between C_J and C_J^top should be introduced in the opening paragraphs for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We respond to each major comment below and will revise the abstract to address the concerns about the strength of the large-N comparison.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the large-N predictions are in 'reasonable agreement' with SO(5) DQCP data rests on the assumption that the QED_3-GNY model at large N faithfully describes the physically relevant small-N regime (N=2 for minimal SO(5)). No estimate of the magnitude of O(1/N^2) corrections or convergence test at N=2 is supplied, so the strength of the comparison cannot be assessed from the given information.

    Authors: We agree that the manuscript provides no estimate of O(1/N^2) corrections and performs no explicit convergence test at N=2. The phrase 'reasonable agreement' reflects our assessment of the numerical proximity between the O(1/N) results and the available DQCP data, but we acknowledge this does not constitute a controlled extrapolation. We will revise the abstract to replace 'are found to be in reasonable agreement' with 'are compared to' the nonperturbative estimates, thereby presenting the large-N results as a benchmark without implying quantitative reliability at small N. revision: yes

  2. Referee: [Abstract] The topological C_J^top is computed only to subleading order at large N, yet the DQCP comparison involves finite-N physics; without a discussion of how higher-order 1/N terms affect the topological contribution when N is lowered, the agreement statement for C_J remains incomplete.

    Authors: The abstract comparison is stated for C_J and C_T at large N; the topological C_J^top is computed separately to O(1/N) and is not part of the quoted agreement claim. We agree that higher-order 1/N corrections to the topological term are not available and that their effect at finite N is therefore unknown. We will add a short qualifying clause in the revised abstract (or a footnote) stating that all central-charge results are obtained at leading 1/N order and that higher-order terms remain to be computed. revision: yes

Circularity Check

0 steps flagged

No significant circularity; computations are independent of target comparison data

full rationale

The paper performs explicit 1/N perturbative calculations of central charges C_J and C_T (and related scaling dimensions) in the QED_d-GNY and scalar QED_d models using standard large-N Feynman diagram techniques. These results are then compared to external, nonperturbative data from conformal bootstrap and fuzzy-sphere simulations for the SO(5) DQCP. No derivation step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation chain; the large-N expansion is controlled within its stated regime and the agreement is presented only as a consistency check against independent sources. The topological C_J^top evaluation is likewise a direct large-N computation without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are described. The 1/N expansion is a standard perturbative tool rather than a fitted parameter introduced in this work.

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Reference graph

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