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Genus 2 Seiberg-Witten curves for rank 2 N=4 superYang-Mills theories
High Energy Physics - Theory · Submitted 22 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute N=4 superYang-Mills theories using the automorphism twist approach.
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The abstract, sentence by sentence
We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute N=4 superYang-Mills theories using the automorphism twist approach. The conformal manifolds of these curves agree with those predicted by S-duality orbits of global structures, and we use this to identify which of the two S-duality orbits of the $so(5) \simeq sp(4)$ superYang-Mills theory the genus-2 curve corresponds to. We also compare the curves to earlier constructions of Seiberg-Witten curves for these theories as spectral curves of integrable systems. These spectral curves have genus greater than the rank, and so only give a Coulomb branch geometry upon projection to a sublattice of the homology lattice of the curves. We show how to determine the correct sublattice projection, and find that the integrable system curves do not apply to our theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute N=4 superYang-Mills theories using the automorphism twist approach. | contribution 0.99 | 0.97 | 0.66 | asserted 1.00 |
| s1 | The conformal manifolds of these curves agree with those predicted by S-duality orbits of global structures, and we use this to identify which of the two S-duality orbits of the $so(5) \simeq sp(4)$ superYang-Mills theory the genus-2 curve corresponds to. | result 0.79 | 0.91 | 0.34 | asserted 1.00 |
| s2 | We also compare the curves to earlier constructions of Seiberg-Witten curves for these theories as spectral curves of integrable systems. | contribution 0.69 | 0.82 | 0.05 | asserted 0.97 |
| s3 | These spectral curves have genus greater than the rank, and so only give a Coulomb branch geometry upon projection to a sublattice of the homology lattice of the curves. | background 0.81 | 0.14 | 0.07 | asserted 1.00 |
| s4 | We show how to determine the correct sublattice projection, and find that the integrable system curves do not apply to our theories. | result 0.92 | 0.95 | 0.39 | asserted 1.00 |
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The paper
Original abstract
We determine new genus 2 Seiberg-Witten curves for four dimensional rank 2 absolute N=4 superYang-Mills theories using the automorphism twist approach. The conformal manifolds of these curves agree with those predicted by S-duality orbits of global structures, and we use this to identify which of the two S-duality orbits of the $so(5) \simeq sp(4)$ superYang-Mills theory the genus-2 curve corresponds to. We also compare the curves to earlier constructions of Seiberg-Witten curves for these theories as spectral curves of integrable systems. These spectral curves have genus greater than the rank, and so only give a Coulomb branch geometry upon projection to a sublattice of the homology lattice of the curves. We show how to determine the correct sublattice projection, and find that the integrable system curves do not apply to our theories.
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How the literature uses it
6 arXiv papers cite this in 10 sentences
Papers citing it · 5 sentences without a confident label
Compares with it 1 paper
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Using the following $_4()$-valued basis change [equation] the period matrix takes the form [equation] By comparing this with [ref] , we see that this is precisely the period matrix for the Jacobian of the curve $y^2=x(x^4+c(τ)x^2+1)$.[This curve is equivalent to the automorphism frame curve found in [ref] through a change of variables.] As this is the Jacobian of a smooth curve, we see that the absolute fibre irreducible as a polarised abelian variety, unlike the other two global forms.
Global forms of $\mathcal{N}=4$ theories and non-minimal Seiberg-Witten solutions · Non-simply laced example · 0.92
Cites it as background 3 papers
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The SW curves for many higher-rank theories and their automorphisms have been studied already from various perspectives [ref] .
Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings · Discussion and overview · 1.00
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A bottom up analysis of $=2$ SCFTs, though far from providing a full classification of these theories, has produced promising results [ref] .
The ABCDEFGJK of maximally strongly coupled $\mathcal{N}=2$ SCFTs · Introduction · 0.94
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With a lower amount of supersymmetry such a complete classification is not available, although promising progress has been made in the last two decades for SCFTs with $≥2$ SUSY [ref] .
Exceptional S-fold SCFTs are almost trivial · Introduction · 0.98
What it cites · 52 sentences without a confident label
Builds on 1 paper
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A similar argument in the $BC_n$ case (almost identical to the one for $F_4$ given in [ref] ) implies that for $BC_2$, the $S_2$ generator acts on the CB again via [ref], but now with $u$ the dimension-2 CB scaling coordinate, and $v$ a certain dimension-4 CB scaling coordinate.
On S-duality for Non-Simply-Laced Gauge Groups · Relation of the conformal manifold to the CB geometry · 0.95
Uses the method or tool of 1 paper
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An alternative way of fixing the reparameterization invariance is to use the $(2,)/_3$ coordinate transformations to put the coefficients of the curve in a standard form, as described in [ref] .
The rank-2 classification problem III: curves with additional automorphisms · SW curves in canonical and automorphism frames · 0.95
Compares with 8 papers
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We will apply this logic to compare the structure of the conformal manifolds of the $A_2$, $G_2$, and non-split $BC_2$, sYM theories as predicted by the curves constructed in section [ref] to the predictions of their S-duality groups from [ref] and [ref] .
On S-duality for Non-Simply-Laced Gauge Groups · Conformal manifolds and S-duality groups · 1.00
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We will apply this logic to compare the structure of the conformal manifolds of the $A_2$, $G_2$, and non-split $BC_2$, sYM theories as predicted by the curves constructed in section [ref] to the predictions of their S-duality groups from [ref] and [ref] .
Reading between the lines of four-dimensional gauge theories · Conformal manifolds and S-duality groups · 1.00
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We will apply this logic to compare the structure of the conformal manifolds of the $A_2$, $G_2$, and non-split $BC_2$, sYM theories as predicted by the curves constructed in section [ref] to the predictions of their S-duality groups from [ref] and [ref] .
S-duality in N=4 supersymmetric gauge theories · Conformal manifolds and S-duality groups · 1.00
Cites as support 2 papers
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For although there exist absolute theories with CBs with complex singularities, they all come from gauging discrete -preserving global symmetries of theories with freely-generated CB chiral rings [ref] .
Gauge theories from principally extended disconnected gauge groups · Introduction · 0.98
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For although there exist absolute theories with CBs with complex singularities, they all come from gauging discrete -preserving global symmetries of theories with freely-generated CB chiral rings [ref] .
Coulomb branches with complex singularities · Introduction · 0.98
Cites as background 25 papers
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The automorphism groups of genus 2 RSs are reviewed in [ref] .
The rank-2 classification problem III: curves with additional automorphisms · SW curves in canonical and automorphism frames · 0.86
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For details, see [ref] .
The rank 2 classification problem I: scale invariant geometries · SW curves in canonical and automorphism frames · 1.00
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The meaning of these restrictions has been described in detail elsewhere, see, e.g., [ref] .
Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2 · Introduction · 0.88
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