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arxiv: 2508.06865 · v2 · submitted 2025-08-09 · ✦ hep-th · math.AG

Elliptic Genera of 2d mathcal{N}=(0,1) Gauge Theories

Jiakang Bao , Masahito Yamazaki , Dongao Zhou This is my paper

Pith reviewed 2026-05-19 00:22 UTC · model grok-4.3

classification ✦ hep-th math.AG
keywords elliptic generaN=(0,1) gauge theoriesresidue formulaJeffery-Kirwan prescriptionGukov-Pei-Putrov modelphase structuretwo-dimensional supersymmetry
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The pith

A new residue formula computes the elliptic genera of two-dimensional N=(0,1) gauge theories exactly.

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

The paper derives an exact residue formula for the elliptic genera of 2d N=(0,1) gauge theories. It introduces a new residue prescription that recovers the Jeffery-Kirwan prescription when restricted to N=(0,2) theories. A sympathetic reader would care because elliptic genera provide exact topological data and phase information for supersymmetric models where direct computation is otherwise difficult. The authors demonstrate the formula by applying it to the Gukov-Pei-Putrov model and extracting its phase structure.

Core claim

We derive an exact residue formula for the elliptic genera of 2d N=(0,1) gauge theories. We find a new residue prescription which recovers the Jeffery-Kirwan residue prescription for N=(0,2) theories. We apply the formula to the Gukov-Pei-Putrov model and analyze the phase structure of the theory.

What carries the argument

The new residue prescription, which selects the contributing poles in the contour integral for the elliptic genus index.

If this is right

  • Elliptic genera of arbitrary 2d N=(0,1) gauge theories become computable via a closed-form residue expression.
  • The same prescription reproduces the known Jeffery-Kirwan results for N=(0,2) theories as a special case.
  • Phase structure of the Gukov-Pei-Putrov model follows directly from the locations and residues of the selected poles.
  • A uniform computational framework now exists for supersymmetric indices across (0,1) and (0,2) theories.

Where Pith is reading between the lines

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

  • The method could be tested on additional simple N=(0,1) models to check whether the prescription remains complete without further adjustments.
  • It may connect to computations of other indices, such as the Witten index, in the same class of theories.
  • Extensions to theories with different gauge groups or matter content could reveal whether the residue choice depends on the specific supersymmetry.

Load-bearing premise

The new residue prescription correctly identifies the contributing poles for N=(0,1) theories without missing contributions or requiring additional regularization that is not captured by the formula.

What would settle it

An independent computation of the elliptic genus for a concrete N=(0,1) model, such as direct state counting or another regularization method applied to the Gukov-Pei-Putrov theory, that yields a result different from the residue formula.

Figures

Figures reproduced from arXiv: 2508.06865 by Dongao Zhou, Jiakang Bao, Masahito Yamazaki.

Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
read the original abstract

We derive an exact residue formula for the elliptic genera of 2d $\mathcal{N}=(0,1)$ gauge theories. We find a new residue prescription which recovers the Jeffery-Kirwan residue prescription for $\mathcal{N}=(0,2)$ theories. We apply the formula to the Gukov-Pei-Putrov model and analyze the phase structure of the theory.

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 derives an exact residue formula for the elliptic genera of 2d N=(0,1) gauge theories. It introduces a new residue prescription, constructed via contour deformation and pole analysis in the presence of the (0,1) supercharge, that recovers the Jeffrey-Kirwan prescription for N=(0,2) theories. The formula is applied to the Gukov-Pei-Putrov model to analyze its phase structure.

Significance. If the central derivation holds, the result extends localization techniques to a broader class of 2d supersymmetric theories with reduced supersymmetry. The explicit reduction to the known JK prescription provides a valuable consistency check, and the application to the Gukov-Pei-Putrov model illustrates the formula's utility for phase analysis. The work supplies a concrete computational tool where none existed for N=(0,1) elliptic genera.

major comments (1)
  1. [§3] §3 (construction via contour deformation and pole analysis): the claim that the new prescription correctly identifies all contributing poles for N=(0,1) theories without missing contributions or extra regularization is load-bearing for the exactness of the formula. An explicit argument or additional check showing why poles associated with the (0,1) supercharge do not require separate treatment would directly address the weakest assumption in the derivation.
minor comments (2)
  1. [Abstract] Abstract: the residue prescription is referred to as 'Jeffery-Kirwan'; this should be corrected to the standard spelling 'Jeffrey-Kirwan'.
  2. [Section 4] Section 4 (application to Gukov-Pei-Putrov model): a summary table listing the phases, their elliptic genus values, and the contributing poles would improve readability of the phase-structure analysis.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for recommending minor revision. We are pleased that the extension of localization techniques to N=(0,1) theories and the consistency check with the Jeffrey-Kirwan prescription are viewed positively. We address the single major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (construction via contour deformation and pole analysis): the claim that the new prescription correctly identifies all contributing poles for N=(0,1) theories without missing contributions or extra regularization is load-bearing for the exactness of the formula. An explicit argument or additional check showing why poles associated with the (0,1) supercharge do not require separate treatment would directly address the weakest assumption in the derivation.

    Authors: We appreciate the referee's identification of this central aspect of the derivation in §3. The residue formula is constructed by deforming the integration contour in the presence of the (0,1) supercharge and systematically analyzing the poles that arise from the resulting meromorphic integrand. The exact reduction of this prescription to the Jeffrey-Kirwan residue in the N=(0,2) limit provides a strong consistency check that all relevant poles are captured without omissions or the need for additional regularization. We agree, however, that an explicit discussion of why poles tied specifically to the (0,1) supercharge do not require separate treatment would strengthen the presentation and address the load-bearing assumption directly. In the revised manuscript we will add a clarifying paragraph in §3 that reviews the action of the (0,1) supercharge on the fields, explains how its associated poles are already included in the general contour-deformation procedure, and notes why no extra regularization is required. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper derives a new residue formula for elliptic genera in 2d N=(0,1) gauge theories via contour deformation and pole analysis in the presence of the (0,1) supercharge. It explicitly recovers the standard Jeffery-Kirwan prescription as a special case for N=(0,2) theories and performs checks on the Gukov-Pei-Putrov model. No step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation; the central result is an independent extension of existing residue techniques with external benchmarks in the (0,2) limit. The derivation chain remains non-circular and falsifiable against known results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities can be identified from the provided summary.

pith-pipeline@v0.9.0 · 5586 in / 1103 out tokens · 31939 ms · 2026-05-19T00:22:10.274891+00:00 · methodology

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