The large Nc limit of N=2 super Yang-Mills, fractional instantons and infrared divergences

Frank Ferrari (Princeton University)

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The large Nc limit of N=2 super Yang-Mills, fractional instantons and infrared divergences

High Energy Physics - Theory · Submitted 20 Jun 2001

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

The authors' main claim Our most interesting finding is that the 1/N expansion breaks down at singularities on the moduli space due to severe infrared divergencies, a fact that has remarkable consequences.

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arXiv IDhep-th/0106192 (version 1)

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CitationFrank Ferrari (Princeton University). "The large Nc limit of N=2 super Yang-Mills, fractional instantons and infrared divergences." arXiv:hep-th/0106192 (2001). https://pith.science/paper/IYV37J7E

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.83 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.50 · compares with prior results 0.69 · mentions code or data availability 0.02.

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We investigate the large Nc limit of pure N=2 supersymmetric gauge theory with gauge group SU(Nc) by using the exact low energy effective action. Typical one-complex dimensional sections of the moduli space parametrized by a global complex mass scale v display three qualitatively different regions depending on the ratio between |v| and the dynamically generated scale Lambda. At large |v|/Lambda, instantons are exponentially suppressed as N goes to infinity. When |v| is of order Lambda, singularities due to massless dyons occur. They are densely distributed in rings of calculable thicknesses in the v-plane. At small |v|/Lambda, instantons disintegrate into fractional instantons of charge 1/(2N). These fractional instantons give non-trivial contributions to all orders of 1/N, unlike a planar diagrams expansion which generates a series in 1/N^2, implying the presence of open strings. We have explicitly calculated the fractional instantons series in two representative examples, including the 1/N and 1/N^2 corrections. Our most interesting finding is that the 1/N expansion breaks down at singularities on the moduli space due to severe infrared divergencies, a fact that has remarkable consequences.

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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 investigate the large Nc limit of pure N=2 supersymmetric gauge theory with gauge group SU(Nc) by using the exact low energy effective action.	contribution 0.94	0.94	0.03	asserted 0.97
s1	Typical one-complex dimensional sections of the moduli space parametrized by a global complex mass scale v display three qualitatively different regions depending on the ratio between \|v\| and the dynamically generated scale Lambda.	result 0.77	0.66	0.03	asserted 1.00
s2	At large \|v\|/Lambda, instantons are exponentially suppressed as N goes to infinity.	result 1.00	0.73	0.04	asserted 1.00
s3	When \|v\| is of order Lambda, singularities due to massless dyons occur.	result 1.00	0.61	0.03	asserted 1.00
s4	They are densely distributed in rings of calculable thicknesses in the v-plane.	result 1.00	0.69	0.03	asserted 1.00
s5	At small \|v\|/Lambda, instantons disintegrate into fractional instantons of charge 1/(2N).	result 1.00	0.67	0.05	asserted 1.00
s6	These fractional instantons give non-trivial contributions to all orders of 1/N, unlike a planar diagrams expansion which generates a series in 1/N^2, implying the presence of open strings.	interpretation 0.84	0.71	0.11	asserted 0.94
s7	We have explicitly calculated the fractional instantons series in two representative examples, including the 1/N and 1/N^2 corrections.	contribution 0.72	0.96	0.05	asserted 1.00
s8	Our most interesting finding is that the 1/N expansion breaks down at singularities on the moduli space due to severe infrared divergencies, a fact that has remarkable consequences.	result 0.96	0.95	0.89	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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The paper

Original abstract

We investigate the large Nc limit of pure N=2 supersymmetric gauge theory with gauge group SU(Nc) by using the exact low energy effective action. Typical one-complex dimensional sections of the moduli space parametrized by a global complex mass scale v display three qualitatively different regions depending on the ratio between |v| and the dynamically generated scale Lambda. At large |v|/Lambda, instantons are exponentially suppressed as N goes to infinity. When |v| is of order Lambda, singularities due to massless dyons occur. They are densely distributed in rings of calculable thicknesses in the v-plane. At small |v|/Lambda, instantons disintegrate into fractional instantons of charge 1/(2N). These fractional instantons give non-trivial contributions to all orders of 1/N, unlike a planar diagrams expansion which generates a series in 1/N^2, implying the presence of open strings. We have explicitly calculated the fractional instantons series in two representative examples, including the 1/N and 1/N^2 corrections. Our most interesting finding is that the 1/N expansion breaks down at singularities on the moduli space due to severe infrared divergencies, a fact that has remarkable consequences.

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References

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Cited by 3 Pith papers

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

Double Scaling Limits in Gauge Theories and Matrix Models
hep-th 2006-03 conditional novelty 6.0 of 10

N=1 gauge theories admit large-N double-scaling limits whose interacting sector is governed by the old matrix model, with gravitational F-terms satisfying the KdV hierarchy.
Open Strings from N=4 Super Yang-Mills
hep-th 2002-04 conditional novelty 6.0 of 10

Open strings on spherical D3-branes (giant gravitons) are reconstructed from N=4 super Yang-Mills operators in a Penrose limit, with the leading spectrum matched.
Massive N=2 Gauge Theories at Large N
hep-th 2013-09 accept novelty 5.0 of 10

Massive N=2 gauge theories at large N reduce to solvable matrix models that exhibit quantum phase transitions at finite 't Hooft coupling, including a third-order transition in super-QCD.

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5 arXiv papers cite this in 9 sentences

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Builds on it 1 paper

To find $μ$, we use the integrated form of ([ref]): [equation] Substituting the solution ([ref]) we obtain: [equation] This generalizes the solution of the pure $𝒩=2$ SYM in the 't Hooft limit [ref] $^3$ to the solution of $𝒩=2$ SQCD in the Veneziano limit.

Massive N=2 Gauge Theories at Large N · Super-QCD with $2N_f$ massive hypermultiplets · 0.97

Compares with it 2 papers

Using the asymptotic form of the kernel: [equation] we can see that in the scaling limit the Hilbert kernel scales away, and we are left with the equation [equation] Differentiating this equation twice, we then get: [equation] This equation has a unique normalizable solution: [equation] This can be seen to agree with the eigenvalue density [ref] obtained from Seiberg-Witten theory directly in flat space.

Large N Limit of N=2 SU(N) Gauge Theories from Localization · Large radius · 0.97
The saddle-point equations of the localization matrix model reproduce [ref] in this corner of the phase diagram the large-$N$ solution of $𝒩=2$ SYM, known from the Seiberg-Witten theory [ref] .

Localization and AdS/CFT Correspondence · Massive theory · 0.80

Cites it as background 2 papers

Such a distribution has been considered several times in the literature and its properties have been discussed in various contexts, see for example [ref] .

Modular anomaly equations in N=2* theories and their large-N limit · Large-$N$ limit with a uniform distribution · 0.97
The large-$N$ limit of the latter was investigated in [ref] for pure gauge $𝒩=2$ super-Yang-Mills (SYM).

Massive N=2 Gauge Theories at Large N · Introduction · 0.91

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