Stringy instanton effects in N=2 gauge theories

Alberto Lerda; Daniele Musso; Hossein Ghorbani

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Stringy instanton effects in N=2 gauge theories

Hossein Ghorbani, Daniele Musso, Alberto Lerda

High Energy Physics - Theory · Submitted 6 Dec 2010

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The authors' main claim In the SU(2) theory these terms have the same structure for all instanton numbers and yield a series of non-perturbative corrections to the prepotential.

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We study the non-perturbative effects induced by stringy instantons on N=2 SU}(N) gauge theories in four dimensions, realized on fractional D3 branes in a C^3/Z_3 orientifold. The stringy instantons, corresponding to D(-1) branes that occupy a node of the orientifold quiver diagram where no D3 brane is present, have the right content of zero-modes to produce non-perturbative terms in the four-dimensional effective action. In the SU(2) theory these terms have the same structure for all instanton numbers and yield a series of non-perturbative corrections to the prepotential. We explicitly compute these corrections up to instanton number k=5 using localization methods.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the non-perturbative effects induced by stringy instantons on N=2 SU}(N) gauge theories in four dimensions, realized on fractional D3 branes in a C^3/Z_3 orientifold.	contribution 0.99	0.84	0.10	asserted 0.96
s1	The stringy instantons, corresponding to D(-1) branes that occupy a node of the orientifold quiver diagram where no D3 brane is present, have the right content of zero-modes to produce non-perturbative terms in the four-dimensional effective action.	background 0.49	0.27	0.16	asserted 1.00
s2	In the SU(2) theory these terms have the same structure for all instanton numbers and yield a series of non-perturbative corrections to the prepotential.	result 0.98	0.72	0.28	asserted 1.00
s3	We explicitly compute these corrections up to instanton number k=5 using localization methods.	contribution 0.63	0.96	0.17	asserted 1.00

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Original abstract

We study the non-perturbative effects induced by stringy instantons on N=2 SU}(N) gauge theories in four dimensions, realized on fractional D3 branes in a C^3/Z_3 orientifold. The stringy instantons, corresponding to D(-1) branes that occupy a node of the orientifold quiver diagram where no D3 brane is present, have the right content of zero-modes to produce non-perturbative terms in the four-dimensional effective action. In the SU(2) theory these terms have the same structure for all instanton numbers and yield a series of non-perturbative corrections to the prepotential. We explicitly compute these corrections up to instanton number k=5 using localization methods.

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10 arXiv papers cite this in 46 sentences

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Papers citing it · 31 sentences without a confident label

Builds on it 2 papers

In this paper we generalize the results obtained for SU$(2)$ in [ref] to SU$(N)$ gauge theory.

Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories · Introduction · 1.00
Using a relation between the elementary symmetric polynomials and power sums (see for instance [ref] ) one is able to generalize the results in [ref] to the gauge group SU$(N)$ [ref] .

Gauge-Stringy Instantons in N=2 U(N) Gauge Theories · Introduction · 0.96

Uses its method or tool 1 paper

In order to study instantons in $𝒩=2$, following the model described in [ref] we act the orbifold group $ℤ_3={1,ξ,ξ^-1}$ with $ξ=e^2πi/3$ on the first two complex internal coordinates, so that the geometry of the internal space becomes $ℂ^2 / ℤ_3 ×ℂ$; the third complex coordinate in the internal space therefore remains unchanged by orbifolding.

Gauge-Stringy Instantons in N=2 U(N) Gauge Theories · Gauge-Stringy Set-up · 0.84

Uses its data or values 1 paper

The entire computation was performed in detail in [ref] of which we simply report the results of use here.

Field Theory Interpretation of N=2 Stringy Instantons · Stringy instantons for $N=2$ $Sp(0)×U(N)$ theory · 0.93

Compares with it 1 paper

We see that one single condition on the only free parameter $𝒩_3$ can entirely remove all the singularities; assuming that [equation] the 3-instanton prepotential in the SU$(N)$ gauge theory under consideration is [equation] [equation] [equation] [equation] As already done for lower instanton numbers, we can check the $k=3$ general formula against the special $N=2$ case explicitly obtained in [ref] .

Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories · 3-instanton prepotential $F_3$ · 0.87

Cites it as background 5 papers

The details of the setup under considerations are already extensively illustrated in [ref] , here we only summarize the moduli spectrum in Table [ref].

Stringy Instantons in SU(N) N=2 Non-Conformal Gauge Theories · Description of the setup · 0.96
The details about the supersymmetry content in this model can be found in [ref] .

Gauge-Stringy Instantons in N=2 U(N) Gauge Theories · Gauge-Stringy Set-up · 0.98
Another interesting aspect regards the reduction of the $𝒩=2$ stringy instanton studied in [ref] .

4d/3d reduction of s-confining theories: the role of the "exotic" D instantons · Conclusions · 0.84

What it cites · 39 sentences without a confident label

Builds on 1 paper

In particular, we investigate the gauge theory engineered with stacks of fractional D3 branes in a $ℂ^3/ℤ_3$ orientifold of type IIB preserving $=2$ supersymmetry in four dimensions, and study the corresponding stringy multi-instanton configurations along the lines already discussed in [ref] for the 1-instanton case.

Stringy Instantons at Orbifold Singularities · Introduction and motivations · 0.98

Uses the method or tool of 10 papers

We have computed such non-perturbative effects with the same localization methods [ref] -Losev:2003py [ref] used to find the gauge instanton terms in the $=2$ super Yang-Mills theory predicted by the Seiberg-Witten curve [ref] .

Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory · Introduction and motivations · 0.98
We have computed such non-perturbative effects with the same localization methods [ref] -Losev:2003py [ref] used to find the gauge instanton terms in the $=2$ super Yang-Mills theory predicted by the Seiberg-Witten curve [ref] .

Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD · Introduction and motivations · 0.98
We have computed such non-perturbative effects with the same localization methods [ref] -Losev:2003py [ref] used to find the gauge instanton terms in the $=2$ super Yang-Mills theory predicted by the Seiberg-Witten curve [ref] .

Seiberg-Witten Prepotential From Instanton Counting · Introduction and motivations · 0.98

Compares with 1 paper

For $k=1$, from z1 we have directly [equation] This is the same result obtained in [ref] .

Stringy Instantons at Orbifold Singularities · The non-perturbative prepotential · 1.00

Cites as background 11 papers

This is usually called the $Ω$-background deformation [ref] -Losev:2003py [ref] which, in our stingy context, can be realized by turning on a non-trivial Ramond-Ramond 3-form flux as discussed in detail in [ref] and more recently in [ref] where the equivalence between the $Ω$-background and the Ramond-Ramond flux has been shown in full generality.

N=2 Instanton Effective Action in Omega-background and D3/D(-1)-brane System in R-R Background · Deformed moduli action · 0.87
This is usually called the $Ω$-background deformation [ref] -Losev:2003py [ref] which, in our stingy context, can be realized by turning on a non-trivial Ramond-Ramond 3-form flux as discussed in detail in [ref] and more recently in [ref] where the equivalence between the $Ω$-background and the Ramond-Ramond flux has been shown in full generality.

Instanton calculus in R-R background and the topological string · Deformed moduli action · 0.87
This is usually called the $Ω$-background deformation [ref] -Losev:2003py [ref] which, in our stingy context, can be realized by turning on a non-trivial Ramond-Ramond 3-form flux as discussed in detail in [ref] and more recently in [ref] where the equivalence between the $Ω$-background and the Ramond-Ramond flux has been shown in full generality.

Seiberg-Witten Prepotential From Instanton Counting · Deformed moduli action · 0.87

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