Nahm's equations, $N=1^*$ domain walls, and D-strings in $AdS_5 x S_5$

B. Pioline; C. Bachas; J. Hoppe

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Nahm's equations, $N=1^*$ domain walls, and D-strings in $AdS_5 x S_5$

C. Bachas, J. Hoppe, B. Pioline

High Energy Physics - Theory · Submitted 9 Jul 2000

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

The authors' main claim We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions.

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arXiv IDhep-th/0007067 (version 4)

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CitationB. Pioline, C. Bachas, J. Hoppe. "Nahm's equations, $N=1^*$ domain walls, and D-strings in $AdS_5 x S_5$." arXiv:hep-th/0007067 (2000). https://pith.science/paper/SRFHZDB6

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.02.

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We consider the following two problems: classical domain walls in the $N=1^*$ mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence. We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions. We argue that general `fuzzy sphere' configurations of D-strings in AdS$_5$ correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider the following two problems: classical domain walls in the $N=1^*$ mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence.	background 0.75	0.51	0.04	unclear 0.57
s1	We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions.	contribution 0.66	0.95	0.54	asserted 1.00
s2	We argue that general `fuzzy sphere' configurations of D-strings in AdS$_5$ correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory.	interpretation 0.88	0.81	0.45	asserted 0.41

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.88.

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arXiv listing abstract v4

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The paper

Original abstract

We consider the following two problems: classical domain walls in the $N=1^*$ mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence. We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions. We argue that general `fuzzy sphere' configurations of D-strings in AdS$_5$ correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory.

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References

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Cited by 5 Pith papers

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

Brane Webs and Magnetic Quivers for SQCD
hep-th 2019-09 conditional novelty 7.0 of 10

The reduced Higgs branch of SU(Nc) SQCD with Nf flavors is a union of mesonic and baryonic cones, each the Coulomb branch of a magnetic quiver read from a five-brane web.
IIB Duals of D=3 N=4 Circular Quivers
hep-th 2012-10 accept novelty 7.0 of 10

Explicit type-IIB AdS4 backgrounds are built for the 3d N=4 SCFTs of circular quivers, and a large-L limit is shown to reproduce M-theory on AdS4 x S7/(Z_k x Z_k-hat).
Branes and the Kraft-Procesi transition: classical case
hep-th 2017-11 conditional novelty 6.0 of 10

The authors show that Kraft-Procesi transitions between nilpotent orbit closures of orthogonal and symplectic Lie algebras have a Type IIB brane realization with O3-planes, and give a matrix algorithm to compute them.
Branes and the Kraft-Procesi Transition
hep-th 2016-09 conditional novelty 5.0 of 10

The Type IIB brane Higgs mechanism reproduces the Kraft-Procesi transitions between nilpotent orbit closures of sl_N, and a two-row matrix encoding of brane configurations computes the full Hasse diagram.
TASI Lectures on Solitons
hep-th 2005-09 accept novelty 3.0 of 10

The lectures give a unified, moduli-space-centered account of instantons, monopoles, vortices and domain walls, showing how each arises from another by dimensional reduction, a scalar vev, or a mass deformation.

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11 arXiv papers cite this in 13 sentences

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Papers citing it · 6 sentences without a confident label

Builds on it 1 paper

There is also a simple modification [ref] of ([ref]), also analytical, which connects the partition $[k/2, k/2]$ to the partition $[k/2 + 1, k/2 - 1]$; in other words, it moves a single block from one row of the diagrams to the next.

Holographic duals of 6d RG flows · Nahm equations · 0.91

Cites it as background 6 papers

For each such curve $h$, the instanton solutions are [equation] The equations ([ref],[ref]) and their solutions have been studied by [ref] , and also [ref] in a different context.

Axial Anomaly in the $SU(N)$ Gauge Matrix Model · Instantons in $SU(N)$ matrix model · 0.87
(Those results are also reviewed nicely in [ref] , where ([ref]) appears in the context of domain walls for the so-called $𝒩=1^*$ field theory in four dimensions.)

Holographic duals of 6d RG flows · Nahm equations · 0.95
The first appearance of these objects in the context of string theory is [ref] , to the best of our knowledge. ] of $𝔰𝔩(N_f , ℂ)$ associated to the partition $ρ^T = (2^N_c,1^N_f-2N_c)$.

Brane Webs and Magnetic Quivers for SQCD · Unitary gauge group · 0.86

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