Calculating the Prepotential by Localization on the Moduli Space of Instantons

Timothy J. Hollowood

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Calculating the Prepotential by Localization on the Moduli Space of Instantons

Timothy J. Hollowood

High Energy Physics - Theory · Submitted 14 Jan 2002

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

The authors' main claim Using this technology we calculate the one- and two-instanton contributions to the prepotential of SU(N) gauge theory with N=2 supersymmetry and show how the localization approach yields the prediction extracted from the Seiberg-Witten curve.

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What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.87 · 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 describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In these situations the instantons are constrained and a potential is generated on the instanton moduli space. Due to existence of a nilpotent fermionic symmetry the resulting integral over the instanton moduli space localizes on the critical points of the potential. Using this technology we calculate the one- and two-instanton contributions to the prepotential of SU(N) gauge theory with N=2 supersymmetry and show how the localization approach yields the prediction extracted from the Seiberg-Witten curve. The technique appears to extend to arbitrary instanton number in a tractable way.

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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 describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches.	contribution 0.97	0.90	0.14	asserted 1.00
s1	In these situations the instantons are constrained and a potential is generated on the instanton moduli space.	background 0.98	0.16	0.05	asserted 1.00
s2	Due to existence of a nilpotent fermionic symmetry the resulting integral over the instanton moduli space localizes on the critical points of the potential.	method 0.97	0.27	0.09	asserted 1.00
s3	Using this technology we calculate the one- and two-instanton contributions to the prepotential of SU(N) gauge theory with N=2 supersymmetry and show how the localization approach yields the prediction extracted from the Seiberg-Witten curve.	result 0.64	0.96	0.74	asserted 1.00
s4	The technique appears to extend to arbitrary instanton number in a tractable way.	interpretation 0.66	0.50	0.15	hedged possibility 0.96

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from proof or derivation 0.99.

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The paper

Original abstract

We describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In these situations the instantons are constrained and a potential is generated on the instanton moduli space. Due to existence of a nilpotent fermionic symmetry the resulting integral over the instanton moduli space localizes on the critical points of the potential. Using this technology we calculate the one- and two-instanton contributions to the prepotential of SU(N) gauge theory with N=2 supersymmetry and show how the localization approach yields the prediction extracted from the Seiberg-Witten curve. The technique appears to extend to arbitrary instanton number in a tractable way.

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References

Forward citations

Cited by 7 Pith papers

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

Seiberg-Witten Prepotential From Instanton Counting
hep-th 2002-06 conditional novelty 9.0 of 10

Equivariant localization on the instanton moduli space yields a closed combinatorial formula for the Seiberg-Witten prepotential, matching known instanton expansions up to five instantons.
Seiberg-Witten Theory and Random Partitions
hep-th 2003-06 accept novelty 8.0 of 10

The low-energy Seiberg-Witten prepotential of N=2 gauge theories is derived from the exact instanton partition function by a saddle-point analysis of random partitions.
Matrix Models, Geometric Engineering and Elliptic Genera
hep-th 2003-10 accept novelty 7.0 of 10

For N=2* theory compactified from six to four dimensions on a torus, matrix models, geometric engineering via the topological vertex, and elliptic-genus instanton calculus all yield the same prepotential, encoded in a...
Small Instantons, Little Strings and Free Fermions
hep-th 2003-02 conditional novelty 7.0 of 10

For the U(1) N=2 gauge theory with all chiral couplings, the partition function equals a free fermion correlator on a sphere and the all-genus topological string free energy on CP^1.
Multi-Instanton Calculus and Equivariant Cohomology
hep-th 2002-11 conditional novelty 6.0 of 10

A supersymmetric localization formula on the ADHM moduli space yields closed sum-over-Young-tableaux expressions for multi-instanton partition functions of N=2, N=2* and N=4 gauge theories.

Show 2 more citing papers

The Calculus of Many Instantons
hep-th 2002-06 accept novelty 4.0 of 10

The paper assembles a unified geometric treatment of multi-instanton calculus, from ADHM moduli spaces to supersymmetric partition functions and D-brane relations.
Two Recursions for the Seiberg-Witten Prepotential: Zamolodchikov's Recursion, the AGT Correspondence and Topological Recursion on the Seiberg-Witten Curve
hep-th 2026-09 reject novelty 2.0 of 10

A review that claims to bridge Zamolodchikov's recursive relation and Nekrasov's partition function via AGT, but does not produce new evidence.

How the literature uses it

6 arXiv papers cite this in 7 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 · 5 sentences without a confident label

Cites it as support 2 papers

Indeed, the $ϕ$ dependence disappears upon integrating over $ℳ_k$ as a consequence of the cohomology properties of the integration measure on the instanton moduli space [ref] .

Instantons in N=2 magnetized D-brane worlds · Instanton induced prepotential and effective action · 0.98
This dependence disappears upon integrating over $ℳ_k$ as a consequence of the cohomology properties of the integration measure on the instanton moduli space [ref] .

(D)-instanton effects in magnetized brane worlds · The stringy instanton calculus · 0.96

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