Magnetic Domains

Christian Saemann; Derek Harland; Sam Palmer

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Magnetic Domains

Derek Harland, Sam Palmer, Christian Saemann

High Energy Physics - Theory · Submitted 30 Apr 2012

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

The authors' main claim We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space.

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What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.71 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.25 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n.	background 1.00	0.08	0.10	speculative 0.60
s1	We interpret these ideas using string theory and present some partial proofs of this conjecture.	contribution 0.84	0.92	0.11	asserted 0.92
s2	We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains.	contribution 1.00	0.91	0.14	asserted 0.99
s3	Bags in four dimensions conjecturally describe the large n limit of n self-dual strings.	background 0.69	0.12	0.17	speculative 0.87
s4	We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space.	result 0.93	0.93	0.24	asserted 1.00
s5	We also formulate our Nahm equations using strong homotopy Lie algebras.	contribution 0.75	0.91	0.09	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.96.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.

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2 arXiv papers cite this in 4 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 · 3 sentences without a confident label

Cites it as support 1 paper

First of all, the notion of a monopole bag together with the associated Nahm construction have been lifted to M-theory [ref] .

M-Brane Models and Loop Spaces · Summary and recent developments · 0.99

What it cites · 62 sentences without a confident label

Builds on 2 papers

We state and prove a Nahm transform for magnetic domains which generalizes that given in [ref] .

1102.30481 · Introduction and results · 0.99
Analogously to the case of magnetic domains in $^3$, we have the following theorem, which refines a result of Dunajski [ref] :

math.DG/0303181 · Nahm transform and its inverse · 0.95

Uses the method or tool of 1 paper

We will now extend the map $i$ to a diffeomorphism $t:×M→Ω^c$ as done in [ref] : The vector field $s$ has the properties [equation] where $$ denotes the Lie derivative.

1102.30481 · Nahm transform for magnetic domains · 0.82

Compares with 2 papers

To compare with Chalmers-Hanany-Witten configurations [ref] , we T-dualize along the $x^4$- and $x^5$-directions, S-dualize and obtain [equation] Dirac monopoles correspond to a single $N=1$ NS5-brane at e.g. $s=0$.

Three Dimensional Gauge Theories and Monopoles · Brane interpretation of magnetic walls and bags · 0.81
To compare with Chalmers-Hanany-Witten configurations [ref] , we T-dualize along the $x^4$- and $x^5$-directions, S-dualize and obtain [equation] Dirac monopoles correspond to a single $N=1$ NS5-brane at e.g. $s=0$.

Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics · Brane interpretation of magnetic walls and bags · 0.81

Cites as support 1 paper

They therefore come with an infinite number of conserved charges as shown in [ref] for magnetic bags.

1102.30481 · Nahm transform for magnetic domains · 0.96

Cites as background 25 papers

In the case of self-dual strings, this is the Basu-Harvey equation [ref] [equation] The functions $T^μ(s)$ take values in a 3-Lie algebra. 3-Lie algebras were introduced by Filippov [ref] and are by definition vector spaces $$ equipped with a 3-bracket $[·,·,·]:^3→$.

The M2-M5 Brane System and a Generalized Nahm's Equation · Nambu-Poisson structure and the Basu-Harvey equation · 0.82
The analog of the Nahm equation for one or two M2-branes is known as the Basu-Harvey equation [ref] , and a generalization to arbitrarily many M2-branes was proposed in [ref] .

0807.01970 · Introduction and results · 0.93
The analog of the Nahm equation for one or two M2-branes is known as the Basu-Harvey equation [ref] , and a generalization to arbitrarily many M2-branes was proposed in [ref] .

0807.10740 · Introduction and results · 0.93

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