A Tale of N Cones

Amihay Hanany; Antoine Bourget; Julius F. Grimminger; Marcus Sperling; Rudolph Kalveks; Zhenghao Zhong

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A Tale of N Cones

Antoine Bourget, Julius F. Grimminger, Amihay Hanany, Rudolph Kalveks, Marcus Sperling, Zhenghao Zhong

High Energy Physics - Theory · Submitted 29 Mar 2023

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

The authors' main claim We propose the Hasse diagrams of the full quantum moduli spaces of our theories.

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arXiv ID2303.16939 (version 2)

Pith IDMDII75ZF, Pith's permanent record of this paper and its review

CitationAmihay Hanany, Antoine Bourget, Julius F. Grimminger, Marcus Sperling, Rudolph Kalveks, Zhenghao Zhong. "A Tale of N Cones." arXiv:2303.16939 (2023). https://pith.science/paper/MDII75ZF

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.87 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study particular families of bad 3d $\mathcal{N}=4$ quiver gauge theories, whose Higgs branches consist of many cones. We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone. Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches. These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring). Applying the principle of \emph{inversion} to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams. These Coulomb branches have several most singular loci, corresponding to the the several cones in the Higgs branch. We propose the Hasse diagrams of the full quantum moduli spaces of our theories. The quivers we study can be taken to be 5d effective gauge theories living on brane webs. Their infinite coupling theories have Higgs branches which also consist of multiple cones. Some of these cones have \emph{decorated} magnetic quivers, whose 3d Coulomb branches remain elusive.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study particular families of bad 3d $\mathcal{N}=4$ quiver gauge theories, whose Higgs branches consist of many cones.	contribution 0.89	0.84	0.08	asserted 0.99
s1	We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone.	contribution 0.72	0.93	0.18	asserted 1.00
s2	Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches.	method 0.93	0.93	0.07	asserted 0.99
s3	These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring).	result 0.99	0.79	0.11	asserted 1.00
s4	Applying the principle of \emph{inversion} to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams.	contribution 0.59	0.75	0.22	speculative 1.00
s5	These Coulomb branches have several most singular loci, corresponding to the the several cones in the Higgs branch.	result 0.86	0.68	0.12	asserted 1.00
s6	We propose the Hasse diagrams of the full quantum moduli spaces of our theories.	contribution 0.76	0.89	0.40	asserted 0.55
s7	The quivers we study can be taken to be 5d effective gauge theories living on brane webs.	method 0.46	0.34	0.03	hedged possibility 0.59
s8	Their infinite coupling theories have Higgs branches which also consist of multiple cones.	result 0.81	0.60	0.06	asserted 1.00
s9	Some of these cones have \emph{decorated} magnetic quivers, whose 3d Coulomb branches remain elusive.	limitation 0.78	0.36	0.05	asserted 0.93

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.58.

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arXiv listing abstract v2

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We study particular families of bad 3d $\mathcal{N}=4$ quiver gauge theories, whose Higgs branches consist of many cones. We show the role of a novel brane configuration in realizing the Higgs moduli for each distinct cone. Through brane constructions, magnetic quivers, Hasse diagrams, and Hilbert series computations we study the intricate structure of the classical Higgs branches. These Higgs branches are both non-normal (since they consist of multiple cones) and non-reduced (due to the presence of nilpotent operators in the chiral ring). Applying the principle of \emph{inversion} to the classical Higgs branch Hasse diagrams, we conjecture the quantum Coulomb branch Hasse diagrams. These Coulomb branches have several most singular loci, corresponding to the the several cones in the Higgs branch. We propose the Hasse diagrams of the full quantum moduli spaces of our theories. The quivers we study can be taken to be 5d effective gauge theories living on brane webs. Their infinite coupling theories have Higgs branches which also consist of multiple cones. Some of these cones have \emph{decorated} magnetic quivers, whose 3d Coulomb branches remain elusive.

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How the literature uses it

10 arXiv papers cite this in 24 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 · 14 sentences without a confident label

Uses its method or tool 1 paper

We compute the Hilbert series for the union of the Coulomb branches of a set of quivers ${Q_i}$, where $i=1,⋯,n$, using the Unions of Cones formula [ref] : [equation]

Quotient Quiver Subtraction · Rules for $(n)$ HKQ by quotient quiver subtraction · 1.00

Compares with it 1 paper

In both cases, we get an $𝒩=4$ SQED with two flavors, which is compatible with the findings of [ref] .

Probing bad theories with the dualization algorithm II · Electric dual · 0.92

Cites it as background 4 papers

* Recent advancements in the understanding of the Higgs branch (HB) structure of higher-dimensional quiver gauge theories with 8 supercharges by means of Coulomb branches (CBs) of magnetic quivers (MQs) associated to 3D $N=4$ gauge theories, [ref] .

Drinfeld Centers from Magnetic Quivers · Introduction · 0.97
The notion of magnetic quivers has been applied to quantum field theories with eight supercharges in three, four, five, and six dimensions with great success [ref] .

Quotient Quiver Subtraction · Introduction · 0.97
A proposal for the full moduli space of the bad $SU(N_c)$ SQCD with $N_f$ flavors has been recently made in [ref] , based on the conjecture that the quantum Coulomb branch can be obtained by a procedure called inversion of the classical Higgs branch [ref] .

Probing bad theories with the dualization algorithm II · Introduction · 0.85

What it cites · 101 sentences without a confident label

Uses the method or tool of 6 papers

Based on inversion [ref] of the classical Higgs branch Hasse diagram, we conjecture the quantum Coulomb branch and full moduli space Hasse diagrams for the 3d $𝒩=4$ theories studied in this paper.

Hasse Diagrams for $\mathbf{3d}$ $\mathbf{\mathcal{N}=4}$ Quiver Gauge Theories -- Inversion and the full Moduli Space · Introduction and Summary · 0.93
Note that using the quiver subtraction algorithm [ref] on the magnetic quivers to obtain the Hasse diagram of the Higgs branch of [ref] yields [ref].

The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities · New Higgs Phases from Old Brane Systems · 0.84
The relevant brane web, after resolving an O7$^-$ plane [ref] and suitable Hanany-Witten transitions, is: [equation] We can use the rules developed in [ref] to read off the magnetic quivers from maximal subdivisions of the web.

F-theory and Orientifolds · New Higgs Phases from Old Brane Systems · 0.93

Compares with 3 papers

We can propose the following Hasse diagram for the Coulomb branch of [ref]: [equation] This is consistent with the description of the Coulomb branch of [ref] computed in [ref] via the BFN construction and given in terms of generalized affine Grassmannian slices, and computed in [ref] via abelianisation.

Coulomb branches of $3d$ $\mathcal N=4$ quiver gauge theories and slices in the affine Grassmannian (with appendices by Alexander Braverman, Michael Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Hiraku Nakajima, Ben Webster, and Alex Weekes) · U(k) SQCD · 0.85
We can propose the following Hasse diagram for the Coulomb branch of [ref]: [equation] This is consistent with the description of the Coulomb branch of [ref] computed in [ref] via the BFN construction and given in terms of generalized affine Grassmannian slices, and computed in [ref] via abelianisation.

The Infrared Physics of Bad Theories · U(k) SQCD · 0.85
This is the analysis presented in [ref] ,[We do not perform an S-duality as it is not necessary for reading magnetic quivers.] and matches [ref].

A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours · A Tale of Two Cones · 0.80

Cites as background 14 papers

The quantum moduli space of [ref] as a 4d $𝒩=2$ theory was explored in [ref] .

The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD · SU(k) SQCD · 0.87
The classical Higgs branch of this theory was studied in detail in [ref] .

Brane Webs and Magnetic Quivers for SQCD · SU(k) SQCD · 0.87
This theory was studied extensively in [ref] .

The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories · USp(2k) SQCD · 0.94

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