Simple Singularities and N=2 Supersymmetric Yang-Mills Theory

A. Klemm; S. Theisen; S. Yankielowicz; W. Lerche

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Simple Singularities and N=2 Supersymmetric Yang-Mills Theory

A. Klemm, W. Lerche, S. Theisen, S. Yankielowicz

High Energy Physics - Theory · Submitted 7 Nov 1994

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to underly the quantum moduli space of $SU(n)$ N=2 supersymmetric gauge theory.

how it is stated · asserted 0.45 read the record →

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arXiv IDhep-th/9411048 (version 3)

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CitationA. Klemm, S. Theisen, S. Yankielowicz, W. Lerche. "Simple Singularities and N=2 Supersymmetric Yang-Mills Theory." arXiv:hep-th/9411048 (1994). https://pith.science/paper/5OW4QG3J

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What the abstract itself states, as probabilities: claims first 0.31 · states limitation 0.59 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.66 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to underly the quantum moduli space of $SU(n)$ N=2 supersymmetric gauge theory. These curves have an obvious generalization to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities. To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced. We also give some remarks on a possible relation to string theory.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups.	contribution 0.73	0.83	0.11	asserted 0.96
s1	Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to underly the quantum moduli space of $SU(n)$ N=2 supersymmetric gauge theory.	contribution 0.97	0.90	0.38	asserted 0.45
s2	These curves have an obvious generalization to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities.	contribution 0.87	0.66	0.17	asserted 0.99
s3	To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced.	result 0.84	0.86	0.13	asserted 0.81
s4	We also give some remarks on a possible relation to string theory.	interpretation 0.65	0.68	0.03	hedged possibility 0.84

What kind of paper the classifier reports this is: theoretical result 0.75 · evidence from argument 0.86.

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The paper

Original abstract

We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to underly the quantum moduli space of $SU(n)$ N=2 supersymmetric gauge theory. These curves have an obvious generalization to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities. To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced. We also give some remarks on a possible relation to string theory.

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How later papers used it

46 later papers cite it

Evidence: some. 44 of the citing papers share no author with it, and 4 of those carry a confident label from Pith's citation classifier.

Pith read 6 of the 70 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 built on it.

Builds on it 1 of 2 papers with this label · 1 by the same authors

By the same authors

Based the first term in its curve on this paper's pure SU(N) generalization.

The Omega deformed B-model for rigid N=2 theories (2011) (same authors) · 0.90 · paraphrased: the licence does not allow quoting

How the literature uses it

45 arXiv papers cite this in 69 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 41 sentences without a confident label

Contests it 1 paper

For this, one needs to match the $F_4$ expansions with the leading coefficients of the (differentiated) prepotential [ref] = τ_0/6∑_i=1^3Z_i^2+_1-loop+_inst., where[We correct a typo in [ref] .] τ_0 =9-log4/2πi.

Elliptic Loci of SU(3) Vacua · Picard-Fuchs system for large $v$ · contest 0.90

Builds on it 2 papers

The general-$N$ statements (sw_curve_admits_effective_theory, sw_effective_theory_unique_up_to_duality, extended to $SU(N)$ in [ref] ) are proved in the same repository from one consolidated period input, periodRigidityAxiom (the Gauss–Manin / Picard–Fuchs period-variation theorem); constructing that higher-genus period geometry is future work (6, B.1).

Axioms for physical reasoning: codifying the Seiberg--Witten solution in Lean · What is proved · 0.83
The first term in this curve is based on the pure $SU(N)$ generalization [ref] [ref] of [ref] , while the mass dependent terms are fixed by requiring the correct residua of the Seiberg-Witten differential.

The Omega deformed B-model for rigid N=2 theories · The $SU(N)$ $N_f=2N$ curves · 0.90

Uses its method or tool 2 papers

The metric on the moduli space can be computed from the curve $C$ [ref] :

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In appendix [ref] we derive $(a^(N_F,k)_D,a^(N_F,k))$ and $F^(N_F,k)$ using the latter method, following [ref] , and in particular the solutions in particular [ref] .

Phase Transitions at Unusual Values of $\theta$ · Singularity Structure · 0.97

Compares with it 1 paper

We note that is also the Weierstrass form for the Seiberg-Witten curve for pure $SU(2)$ gauge theory as quoted in [ref] , while if we transform the $N_f=0$ case [ref] in ([ref]) into Weierstrass form we obtain [equation] The two curves specified by ([ref]) with ([ref]) or ([ref]) respectively are known to be isogeneous.

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Cites it as background 17 papers

As is well known from the work of Seiberg and Witten [ref] and its generalizations [ref] , the low-energy description of the $=2$ theory involves a Coulomb branch of vacua, parametrized by $N-1$ holomorphic moduli $u_I = (ϕ^I)$ with $I=2, …, N$.

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The low energy effective theory (and the quantum Coulomb moduli space) of $=2$ supersymmetric gauge theory is described by the Seiberg-Witten curve and the meromorphic one-form called Seiberg-Witten one-form [ref] .

The Quiver Matrix Model and 2d-4d Conformal Connection · $=2$ gauge theory and Seiberg-Witten curve · 0.97
We first recall the Seiberg-Witten geometry in Section [ref] following [ref] .

Elliptic Loci of SU(3) Vacua · The Coulomb branch of the $SU(3)$ theory · 0.89

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