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Holographic non-perturbative corrections to gauge couplings
High Energy Physics - Theory · Submitted 10 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory.
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The abstract, sentence by sentence
We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I' theory by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7's. The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring. Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background. This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I', namely of the N=2, Sp(1) SYM theory with Nf=4. Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory. They also explain the recent observation that the exact coupling for this theory can be entirely reconstructed from its perturbative part plus the knowledge of the chiral ring on the D7 branes supporting its flavor degrees of freedom.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I' theory by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7's. | contribution 0.92 | 0.95 | 0.28 | asserted 1.00 |
| s1 | The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring. | result 0.84 | 0.84 | 0.10 | asserted 1.00 |
| s2 | Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background. | method 0.70 | 0.86 | 0.18 | asserted 1.00 |
| s3 | This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I', namely of the N=2, Sp(1) SYM theory with Nf=4. | interpretation 0.79 | 0.73 | 0.23 | asserted 1.00 |
| s4 | Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory. | result 0.56 | 0.95 | 0.53 | asserted 1.00 |
| s5 | They also explain the recent observation that the exact coupling for this theory can be entirely reconstructed from its perturbative part plus the knowledge of the chiral ring on the D7 branes supporting its flavor degrees of freedom. | interpretation 0.94 | 0.63 | 0.28 | asserted 0.99 |
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The paper
Original abstract
We give a direct microscopic derivation of the F-theory background that corresponds to four D7 branes of type I' theory by taking into account the D-instanton contributions to the emission of the axio-dilaton field in the directions transverse to the D7's. The couplings of the axio-dilaton to the D-instanton moduli modify its classical source terms which are shown to be proportional to the elements of the D7 brane chiral ring. Solving the bulk field equations with the non-perturbatively corrected sources yields the full F-theory background. This solution represents the gravitational dual of the four-dimensional theory living on a probe D3 brane of type I', namely of the N=2, Sp(1) SYM theory with Nf=4. Our results provide an explicit microscopic derivation of the non-perturbative gravitational dual of this theory. They also explain the recent observation that the exact coupling for this theory can be entirely reconstructed from its perturbative part plus the knowledge of the chiral ring on the D7 branes supporting its flavor degrees of freedom.
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References
How the literature uses it
12 arXiv papers cite this in 26 sentences
Papers citing it · 19 sentences without a confident label
Builds on it 1 paper
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This has been done in [ref] for the SO(8) case but it holds in the more general settings under consideration here.
Multi instanton tests of holography · The axion dilaton profile · 0.83
Uses its method or tool 2 papers
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To compute this coupling, let us first consider an instanton disk diagram with $ℓ$ vertices for $χ$ (say of type 0) inserted along the boundary and one vertex for the NS-NS scalar $b$ in the interior, corresponding to the following amplitude [equation] By taking the $b$ vertex in the $(-1,-1)$ picture as in ([ref]), we saturate the superghost number anomaly of the disk and thus we have to take all $χ_0$ vertices in the 0 picture where they are simply [equation] Computing the CFT correlation functions among the vertex operators as discussed in Ref. [ref] , and inserting the topological normalization $π/g_s$ of the instantonic disk, one finds that the amplitude ([ref]) for a given ordering of the open string vertices is [equation] Summing over the $(ℓ-1)!$ inequivalent orderings of the $χ_0$ vertices (all of which give the same contribution), multiplying by the symmetry factor $1/ℓ !$ and
Non-perturbative gauge/gravity correspondence in N=2 theories · Interaction among $t$ and many $χ$'s · 0.91
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This amounts to first define the deformed instanton partition function [equation] where $ϵ_1$ and $ϵ_2$ are deformation parameters which in our string set-up can be introduced by putting the brane system in a graviphoton background [ref] , and then to compute the prepotential according to [equation] The integral appearing in ([ref]) is related to the instanton part of the chiral ring elements $⟨ ϕ_0^ℓ⟩$ of the gauge theory on the D3-branes, which can be computed as [For details on the derivation of this formula we refer to [ref] .] [equation] Notice that the integrals in ([ref]) and ([ref]) are over all moduli including $x$ and $θ$, and that in the limit $ϵ_i →0$ the factor $ϵ_1 ϵ_2$ in ([ref]) compensates for the volume $V∼1/ϵ_1ϵ_2$ of the regularized four dimensional superspace.
Non-perturbative aspects of gauge/gravity duality · The exact $t$ profile emitted by fractional D3-branes and D-instantons · 0.94
Cites it as background 1 paper
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Beyond the instantons/D-instantons calculations that we have already mentioned [ref] , D-instanton corrections to the gravitational background dual to a collection of D-branes have been investigated in [ref] .
Examples of Emergent Type IIB Backgrounds from Matrices · Introduction · 0.98
What it cites · 43 sentences without a confident label
Uses the method or tool of 6 papers
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We demonstrate in Section [ref] that the relevant integrals coincide with the ones that compute the non-perturbative corrections to the elements of the chiral ring on the D7 branes, namely to the vacuum expectation values of the traces of the powers of the adjoint D7/D7 scalar; these integrals can be computed by means of localization techniques [ref] .
Exotic prepotentials from D(-1)D7 dynamics · Introduction · 0.96
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In order to perform the integral over the instanton moduli space and obtain explicit results at instanton number $k$, we have to exploit the localization formulas and adopt Nekrasov's approach to the multi-instanton calculus [ref] (see also Ref.s [ref] Bruzzo:2002xf - [ref] ).
Seiberg-Witten Prepotential From Instanton Counting · Axio-dilaton couplings in the D-instanton action · 1.00
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In order to perform the integral over the instanton moduli space and obtain explicit results at instanton number $k$, we have to exploit the localization formulas and adopt Nekrasov's approach to the multi-instanton calculus [ref] (see also Ref.s [ref] Bruzzo:2002xf - [ref] ).
An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential · Axio-dilaton couplings in the D-instanton action · 1.00
Uses data or values from 1 paper
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We thus can write [equation] so that jnporb becomes [equation] For completeness we report, in our conventions, the explicit expressions of $⟨m^J⟩_n.p.$ for the first few values of $J$ and the first few instanton numbers, that have been computed in Ref. [ref] , namely [equation] where $m=m_1m_2$.
Exotic prepotentials from D(-1)D7 dynamics · The non-perturbative axio-dilaton source · 0.91
Compares with 2 papers
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Introducing the quantity [equation] which in the holographic correspondence parametrizes the Coulomb branch of the dual $=2$ SU(2)$∼$Sp(1) gauge theory, and adding to $τ_n.p.$ the classical contribution ([ref]), we can exhibit the resulting axio-dilaton $τ$ as an expansion in inverse powers of $a$, namely [equation] As shown in Ref. [ref] , this is in perfect agreement with the effective coupling derived from the SW curve for the SU(2) $N_f=4$ theory [ref] .
F-theoretic vs microscopic description of a conformal N=2 SYM theory · The $τ$ profile · 0.97
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Introducing the quantity [equation] which in the holographic correspondence parametrizes the Coulomb branch of the dual $=2$ SU(2)$∼$Sp(1) gauge theory, and adding to $τ_n.p.$ the classical contribution ([ref]), we can exhibit the resulting axio-dilaton $τ$ as an expansion in inverse powers of $a$, namely [equation] As shown in Ref. [ref] , this is in perfect agreement with the effective coupling derived from the SW curve for the SU(2) $N_f=4$ theory [ref] .
Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD · The $τ$ profile · 0.97
Cites as background 18 papers
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Matching the realization of the $𝒩=4$ super Yang-Mills theory by means of open strings attached to D3 branes in flat space with its closed string description led Maldacena [ref] to conjecture the equivalence of this gauge theory to type IIB string theory on $AdS_5×S_5$; within this framework it was soon understood how to holographically relate gauge theory correlators to bulk amplitudes [ref] .
The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 1.00
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Matching the realization of the $𝒩=4$ super Yang-Mills theory by means of open strings attached to D3 branes in flat space with its closed string description led Maldacena [ref] to conjecture the equivalence of this gauge theory to type IIB string theory on $AdS_5×S_5$; within this framework it was soon understood how to holographically relate gauge theory correlators to bulk amplitudes [ref] .
Anti De Sitter Space And Holography · Introduction · 1.00
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Matching the realization of the $𝒩=4$ super Yang-Mills theory by means of open strings attached to D3 branes in flat space with its closed string description led Maldacena [ref] to conjecture the equivalence of this gauge theory to type IIB string theory on $AdS_5×S_5$; within this framework it was soon understood how to holographically relate gauge theory correlators to bulk amplitudes [ref] .
Gauge Theory Correlators from Non-Critical String Theory · Introduction · 1.00
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