Half--Hypers and Quivers

Michele Del Zotto; Sergio Cecotti

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Half--Hypers and Quivers

Sergio Cecotti, Michele Del Zotto

High Energy Physics - Theory · Submitted 10 Jul 2012

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

The authors' main claim For models with gauge group SU(2) x SO(2n) and matter in the half (2,2n) we find strongly coupled chambers with a BPS spectrum consisting of just finitely many hypermultiplets.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.07 · mentions code or data availability 0.02.

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We study systematically the BPS spectra of N=2 SYM coupled to half--hypermultiplets, the basic example being E_7 SYM coupled to a half--hyper in the 56 irrepr. In order to do this, we determine the BPS quivers with superpotential of such N=2 models using a new technique we introduce. The computation of the BPS spectra in the various chambers is then reduced to the Representation Theory of the resulting quivers. We use the quiver description to study the BPS spectrum at both strong and weak coupling. The following models are discussed in detail: SU(6) SYM coupled to a half 20, SO(12) SYM coupled to a half 32, and E_7 SYM coupled to a half 56. For models with gauge group SU(2) x SO(2n) and matter in the half (2,2n) we find strongly coupled chambers with a BPS spectrum consisting of just finitely many hypermultiplets.

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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 systematically the BPS spectra of N=2 SYM coupled to half--hypermultiplets, the basic example being E_7 SYM coupled to a half--hyper in the 56 irrepr.	contribution 0.94	0.89	0.08	asserted 0.97
s1	In order to do this, we determine the BPS quivers with superpotential of such N=2 models using a new technique we introduce.	method 0.84	0.95	0.05	asserted 1.00
s2	The computation of the BPS spectra in the various chambers is then reduced to the Representation Theory of the resulting quivers.	method 0.99	0.83	0.13	asserted 1.00
s3	We use the quiver description to study the BPS spectrum at both strong and weak coupling.	method 0.61	0.94	0.07	asserted 1.00
s4	The following models are discussed in detail: SU(6) SYM coupled to a half 20, SO(12) SYM coupled to a half 32, and E_7 SYM coupled to a half 56.	contribution 0.95	0.82	0.06	asserted 0.99
s5	For models with gauge group SU(2) x SO(2n) and matter in the half (2,2n) we find strongly coupled chambers with a BPS spectrum consisting of just finitely many hypermultiplets.	result 1.00	0.95	0.22	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.87 · evidence from proof or derivation 0.97.

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The paper

Original abstract

We study systematically the BPS spectra of N=2 SYM coupled to half--hypermultiplets, the basic example being E_7 SYM coupled to a half--hyper in the 56 irrepr. In order to do this, we determine the BPS quivers with superpotential of such N=2 models using a new technique we introduce. The computation of the BPS spectra in the various chambers is then reduced to the Representation Theory of the resulting quivers. We use the quiver description to study the BPS spectrum at both strong and weak coupling. The following models are discussed in detail: SU(6) SYM coupled to a half 20, SO(12) SYM coupled to a half 32, and E_7 SYM coupled to a half 56. For models with gauge group SU(2) x SO(2n) and matter in the half (2,2n) we find strongly coupled chambers with a BPS spectrum consisting of just finitely many hypermultiplets.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Infinitely many N=2 SCFT with ADE flavor symmetry
hep-th 2012-10 conditional novelty 7.0 of 10

For each ADE Lie group G, an infinite tower of 4D N=2 SCFTs D(G,s) is argued to exist, with flavor symmetry G and beta-function contribution s/[2(s+1)] adjoint hypermultiplets.
Geometric engineering of (framed) BPS states
hep-th 2013-01 conditional novelty 6.0 of 10

Geometric engineering reproduces the SU(N) BPS quiver and yields a conjectural equivalence between the field-theory BPS spectrum and large-radius D-brane bound states, plus a recursive Donaldson-Thomas algorithm for B...

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12 arXiv papers cite this in 41 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 · 29 sentences without a confident label

Uses its method or tool 1 paper

There is a general first principle strategy to find the quiver of a $=2$ gauge theory (if it exists at all), namely the Dirac integrality conditions [ref] .

4d N=2 Gauge Theories and Quivers: the Non-Simply Laced Case · $Q$–systems and Dirac integrality conditions · 0.89

Cites it as background 7 papers

In the last year there has been significant progress in the computation of BPS spectra of 4d $=2$ supersymmetric gauge theories using the Representation Theory of quivers with superpotentials [ref] (for previous work see [ref] ; for other approches to the $=2$ BPS spectra see [ref] ).

4d N=2 Gauge Theories and Quivers: the Non-Simply Laced Case · Introduction · 0.93
Recent physics results on BPS states [ref] point towards a general conjectural correspondence assigning to an $=2$ supersymmetric gauge theory $(i)$ a triangulated CY3 category $$, and $(ii)$ a map $ϱ: →Stab()$ from the universal cover $$ of the gauge theory Coulomb branch to the moduli space of Bridgeland stability conditions on $$.

Geometric engineering of (framed) BPS states · A (short) summary for mathematicians · 0.80
One is geometrical, relying upon spectral networks [ref] , the other is algebraic and it is based on BPS quivers, motivated by geometric engineering in Type II superstrings [ref] .

Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I · Introduction · 0.83

What it cites · 85 sentences without a confident label

Uses the method or tool of 22 papers

In this section we determine the spectrum of the simplest half-hypers models in a strongly coupled chamber by means of the mutation method of [ref] (for a mathematical interpretation see [ref] ).

N=2 Quantum Field Theories and Their BPS Quivers · BPS spectrum at strong coupling: First results · 1.00
In this section we determine the spectrum of the simplest half-hypers models in a strongly coupled chamber by means of the mutation method of [ref] (for a mathematical interpretation see [ref] ).

Cluster algebras and derived categories · BPS spectrum at strong coupling: First results · 1.00
[ref] which gives the correct quiver provided the $=2$ theory with gauge group $G$ and the given quark representation $R$ is a quiver gauge theory which, in particular, requires $R$ to be small enough so that the coupled theory remains asymptotically free (see [ref] ).

A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra · The `massive quark' procedure · 0.92

Compares with 1 paper

This description of $ℒ(Q,)$ is parallel to the one given in [ref] for $=2$ SYM coupled to massive hypermultiplets.

A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra · Light BPS particles at weak coupling · 0.97

Cites as support 4 papers

Luckily, the most interesting examples of gauge theories with half–multiplets have a Type IIB engineering, and for these theories the existence of a quiver is garanteed by the $2d/4d$ correspondence [ref] .

R-Twisting and 4d/2d Correspondences · Introduction · 0.98
In particular, this means that such algebras are tame, so the BPS spectrum consists only of hypermultiplets and vector–multiplets, all higher spin states being forbidden [ref] .

A class of ${\rm II_1}$ factors with an exotic abelian maximal amenable subalgebra · $SU(2)^k$ coupled to half–hypers as gentle $=2$ models · 0.97
However, in each (weakly coupled) chamber precisely one representation per root is stable [ref] .

N=2 Quantum Field Theories and Their BPS Quivers · Universality of the YM sector · 0.98

Cites as background 5 papers

[ref] for details) the BPS particles correspond to the susy vacua of a quiver 1d SQM which is specified by a quiver $Q$ and a superpotential $$.

Classification of complete N=2 supersymmetric theories in 4 dimensions · Quivers and representations · 0.83
[ref] for details) the BPS particles correspond to the susy vacua of a quiver 1d SQM which is specified by a quiver $Q$ and a superpotential $$.

BPS Quivers and Spectra of Complete N=2 Quantum Field Theories · Quivers and representations · 0.83
[ref] for details) the BPS particles correspond to the susy vacua of a quiver 1d SQM which is specified by a quiver $Q$ and a superpotential $$.

N=2 Quantum Field Theories and Their BPS Quivers · Quivers and representations · 0.83

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