Generalized ADHM equations from marginal deformations in open superstring field theory

Jakub Vo\v{s}mera

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Generalized ADHM equations from marginal deformations in open superstring field theory

Jakub Vošmera

High Energy Physics - Theory · Submitted 1 Oct 2019

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

The authors' main claim Working within the framework of both the $A_\infty$ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter.

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Working within the framework of both the $A_\infty$ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter. For a specific class of backgrounds, we find that this condition localizes on the boundary of the worldsheet moduli space, thus providing a very simple computational prescription for recovering algebraic constraints (generalized ADHM equations) which need to be satisfied by the moduli. Applying our results to the $\mathrm{D(-1)/D3}$ system, we confirm up to third order that blowing up the size of the D-instanton inside the D3 brane worldvolume is an exact modulus of the full string theory. We also discuss examples of more complicated backgrounds, such as instantons on unresolved ALE spaces, as well as the spiked instantons.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Working within the framework of both the $A_\infty$ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter.	contribution 0.61	0.96	0.33	asserted 1.00
s1	For a specific class of backgrounds, we find that this condition localizes on the boundary of the worldsheet moduli space, thus providing a very simple computational prescription for recovering algebraic constraints (generalized ADHM equations) which need to be satisfied by the moduli.	result 0.81	0.95	0.29	asserted 1.00
s2	Applying our results to the $\mathrm{D(-1)/D3}$ system, we confirm up to third order that blowing up the size of the D-instanton inside the D3 brane worldvolume is an exact modulus of the full string theory.	result 0.99	0.94	0.33	asserted 1.00
s3	We also discuss examples of more complicated backgrounds, such as instantons on unresolved ALE spaces, as well as the spiked instantons.	contribution 0.95	0.75	0.04	asserted 0.64

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Original abstract

Working within the framework of both the $A_\infty$ and the Berkovits open superstring field theory, we derive a necessary and sufficient condition for a Neveu-Schwarz marginal deformation to be exact up to third order in the deformation parameter. For a specific class of backgrounds, we find that this condition localizes on the boundary of the worldsheet moduli space, thus providing a very simple computational prescription for recovering algebraic constraints (generalized ADHM equations) which need to be satisfied by the moduli. Applying our results to the $\mathrm{D(-1)/D3}$ system, we confirm up to third order that blowing up the size of the D-instanton inside the D3 brane worldvolume is an exact modulus of the full string theory. We also discuss examples of more complicated backgrounds, such as instantons on unresolved ALE spaces, as well as the spiked instantons.

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9 arXiv papers cite this in 28 sentences

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Papers citing it · 14 sentences without a confident label

Builds on it 1 paper

We will thereby generalize the results of [ref] (and subsequently of [ref] ) by including on-shell closed string insertions.

Closed string deformations in open string field theory III: ${\cal N}=2$ worldsheet localization · $N=2$ localization of open-closed couplings · 1.00

Compares with it 2 papers

Although we are here talking about closed string amplitudes, the mechanism is completely parallel to the open string case analyzed in [ref] and [ref] .

Localization of effective actions in Heterotic String Field Theory · Introduction and Summary · 0.85
We will notice that our calculation is analogous to (but somewhat simpler than) the calculation of the coupling $S̃_3,0(ψ)$ presented in [ref] and [ref] .

Closed string deformations in open string field theory III: ${\cal N}=2$ worldsheet localization · Proof of [ref] · 0.98

Cites it as support 2 papers

This is generically true when the $=2$ decomposition is available (as we are assuming here), see [ref] or appendix [ref] for a proof.

Localization of effective actions in Heterotic String Field Theory · Auxiliary fields · 0.99
However, it was again argued in [ref] that the OPE of $G_-1/2𝕍_1/2$ with $𝕎_1/2$ does not have integer poles whenever the local $𝒩=1$ superconformal symmetry generated by ${T,G}$ enhances to a global worldsheet $𝒩=2$ superconformal symmetry with the above-described parameters.

Closed string deformations in open string field theory III: ${\cal N}=2$ worldsheet localization · Computing the leading-order tadpole · 0.97

Cites it as background 6 papers

We recall the set-up of [ref] , where the bosonic $X^1,…,X^4$ and fermionic $ψ^1,…,ψ^4$ target coordinates span the euclidean D3 worldvolume.

Closed string deformations in open string field theory III: ${\cal N}=2$ worldsheet localization · Testing the construction with non-commutative instantons · 0.86
On an independent flow, evidence for background independence has emerged, thanks to the plethora of discovered classical solutions (mainly in the case of open strings) and related aspects [ref] .

Localization of effective actions in Heterotic String Field Theory · Introduction and Summary · 0.90
Over the years, we have understood many issues regarding the non-perturbative landscape of SFT classical solutions [ref] and the explicit constructions of complete RNS actions [ref] .

The classical cosmological constant of open-closed string field theory · Introduction and summary · 1.00

What it cites · 81 sentences without a confident label

Uses the method or tool of 6 papers

As we have hinted at above, the core of the first two methods will be the recipe of [ref] , that is, we will assume that we can decompose the string fields $Ψ_1$ and $e$ into eigenstates of the $R$-current $J$ of an $𝒩=2$ worldsheet superconformal algebra ${T,J,G^±}$ with $R$-charge $±1$.

Localization of effective actions in open superstring field theory · Evaluation of the obstruction · 0.99
As we have hinted at above, the core of the first two methods will be the recipe of [ref] , that is, we will assume that we can decompose the string fields $Ψ_1$ and $e$ into eigenstates of the $R$-current $J$ of an $𝒩=2$ worldsheet superconformal algebra ${T,J,G^±}$ with $R$-charge $±1$.

Supersymmetry Restoration in Superstring Perturbation Theory · Evaluation of the obstruction · 0.99
As we have hinted at above, the core of the first two methods will be the recipe of [ref] , that is, we will assume that we can decompose the string fields $Ψ_1$ and $e$ into eigenstates of the $R$-current $J$ of an $𝒩=2$ worldsheet superconformal algebra ${T,J,G^±}$ with $R$-charge $±1$.

Localization of effective actions in open superstring field theory: small Hilbert space · Evaluation of the obstruction · 0.99

Compares with 4 papers

We can also check the validity of the intermediate manipulations we have performed so far by comparing [ref] with the Berkovits-like form of the quartic part of the classical effective action of [ref] .

Localization of effective actions in open superstring field theory · $𝒪_2$ terms · 1.00
We can also check the validity of the intermediate manipulations we have performed so far by comparing [ref] with the Berkovits-like form of the quartic part of the classical effective action of [ref] .

Localization of effective actions in open superstring field theory: small Hilbert space · $𝒪_2$ terms · 1.00
They also compute open string gauge field profiles for the finite-size $SU(2)$ instanton and compare their result with the findings of [ref] .

Classical gauge instantons from open strings · Discussion and outlook · 0.98

Cites as support 1 paper

In particular, we will use the results of [ref] to argue that it holds for all $h=1/2$ NS states whenever the initial open superstring background conserves at least two spacetime supercharges with the same chirality in two non-compact dimensions.

Spacetime supersymmetry in low-dimensional perturbative heterotic compactifications · Marginal deformations in the $A_∞$ OSFT · 0.97

Cites as background 14 papers

In this paper we will focus on the NS sector of the $A_∞$ open superstring field theory [ref] and the Berkovits (WZW-like) open superstring field theory [ref] .

Super-Poincare Invariant Superstring Field Theory · Introduction and summary · 0.84
In this paper we will focus on the NS sector of the $A_∞$ open superstring field theory [ref] and the Berkovits (WZW-like) open superstring field theory [ref] .

Resolving Witten's Superstring Field Theory · Introduction and summary · 0.84
It is a widely accepted conjecture that classical solutions of open superstring field theory[Over the past three decades, several constructions of open superstring field theory in both NS and R sector appeared in the literature (see [ref] , as well as [ref] for some recent developments).

Open superstring field theory I: gauge fixing, ghost structure, and propagator · Introduction and summary · 1.00

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