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Hyper-K\"ahler with Torsion, T-duality, and Defect (p,q) Five-branes
High Energy Physics - Theory · Submitted 13 Nov 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Throughout this analysis, we understand that the HKT represents a coexistent state of two kinds of five-branes.
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The abstract, sentence by sentence
We investigate a five-branes interpretation of hyper-K\"{a}hler geometry with torsion (HKT). This geometry is obtained by conformal transformation of the Taub-NUT space which represents a Kaluza-Klein five-brane. This HKT would represent an NS5-brane on the Taub-NUT space. In order to explore the HKT further, we compactify one transverse direction, and study the $O(2,2;{\mathbb Z}) = SL(2,{\mathbb Z}) \times SL(2,{\mathbb Z})$ monodromy structure associated with two-torus. Performing the conjugate transformation, we obtain a new solution whose physical interpretation is a defect $(p,q)$ five-brane on the ALG space. Throughout this analysis, we understand that the HKT represents a coexistent state of two kinds of five-branes. This situation is different from composite states such as $(p,q)$ five-branes or $(p,q)$ seven-branes in type IIB theory. We also study the T-dualized system of the HKT. We again find a new solution which also indicates another defect $(p,q)$ five-brane on the ALG space.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate a five-branes interpretation of hyper-K\"{a}hler geometry with torsion (HKT). | contribution 1.00 | 0.90 | 0.09 | asserted 0.86 |
| s1 | This geometry is obtained by conformal transformation of the Taub-NUT space which represents a Kaluza-Klein five-brane. | background 0.34 | 0.42 | 0.06 | asserted 1.00 |
| s2 | This HKT would represent an NS5-brane on the Taub-NUT space. | interpretation 0.99 | 0.47 | 0.11 | asserted 0.72 |
| s3 | In order to explore the HKT further, we compactify one transverse direction, and study the $O(2,2;{\mathbb Z}) = SL(2,{\mathbb Z}) \times SL(2,{\mathbb Z})$ monodromy structure associated with two-torus. | method 0.86 | 0.90 | 0.05 | asserted 0.92 |
| s4 | Performing the conjugate transformation, we obtain a new solution whose physical interpretation is a defect $(p,q)$ five-brane on the ALG space. | result 0.74 | 0.94 | 0.28 | asserted 0.98 |
| s5 | Throughout this analysis, we understand that the HKT represents a coexistent state of two kinds of five-branes. | interpretation 1.00 | 0.58 | 0.39 | asserted 0.96 |
| s6 | This situation is different from composite states such as $(p,q)$ five-branes or $(p,q)$ seven-branes in type IIB theory. | interpretation 0.99 | 0.39 | 0.15 | asserted 1.00 |
| s7 | We also study the T-dualized system of the HKT. | contribution 0.83 | 0.91 | 0.03 | asserted 0.97 |
| s8 | We again find a new solution which also indicates another defect $(p,q)$ five-brane on the ALG space. | result 0.96 | 0.95 | 0.14 | hedged possibility 0.53 |
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The paper
Original abstract
We investigate a five-branes interpretation of hyper-K\"{a}hler geometry with torsion (HKT). This geometry is obtained by conformal transformation of the Taub-NUT space which represents a Kaluza-Klein five-brane. This HKT would represent an NS5-brane on the Taub-NUT space. In order to explore the HKT further, we compactify one transverse direction, and study the $O(2,2;{\mathbb Z}) = SL(2,{\mathbb Z}) \times SL(2,{\mathbb Z})$ monodromy structure associated with two-torus. Performing the conjugate transformation, we obtain a new solution whose physical interpretation is a defect $(p,q)$ five-brane on the ALG space. Throughout this analysis, we understand that the HKT represents a coexistent state of two kinds of five-branes. This situation is different from composite states such as $(p,q)$ five-branes or $(p,q)$ seven-branes in type IIB theory. We also study the T-dualized system of the HKT. We again find a new solution which also indicates another defect $(p,q)$ five-brane on the ALG space.
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How the literature uses it
12 arXiv papers cite this in 13 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 5 papers
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Among other things, an exotic brane in type II string theories known as the $5^2_2$-brane, has been studied intensively [ref] .
Non-geometric Five-branes in Heterotic Supergravity · Introduction · 0.95
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These days the exotic branes have been exhaustively investigated in the framework of supergravity theories [ref] , string worldsheet theories [ref] , worldvolume theories [ref] , extended geometries such as doubled sigma model and double field theory [ref] , $β$-supergravity and its extension [ref] , and other huge number of related works[Of course this classification is not rigorous because they are deeply related to each other.].
Semi-doubled Sigma Models for Five-branes · Introduction · 1.00
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See [ref] for the notation of $5^2_2$.] from the viewpoint of the worldsheet theories [ref] , the background geometries as supergravity solutions [ref] , the supersymmetry conditions [ref] and the world-volume theory [ref] .
World-volume Effective Action of Exotic Five-brane in M-theory · Introduction · 0.98
What it cites · 28 sentences without a confident label
Uses the method or tool of 5 papers
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In order to find an answer of this question, we investigate the configuration ([ref]) by virtue of the monodromy structures as discussed in [ref] .
Defect (p,q) Five-branes · A hyper-Kähler geometry with torsion · 0.94
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We have already known that this technique is also useful to study bound states of defect five-branes [ref] .
Exotic branes and non-geometric backgrounds · Conjugate configurations · 0.80
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We have already known that this technique is also useful to study bound states of defect five-branes [ref] .
Rotating string in doubled geometry with generalized isometries · Conjugate configurations · 0.80
Compares with 1 paper
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Again we find that the monodromy matrices $Ω_τ^TdHKT$ and $Ω_ρ^TdHKT$ are equal to those of the defect KK5-brane of another type and of the exotic $5^2_2$-brane, respectively (see [ref] and appendix [ref]).
Defect (p,q) Five-branes · Monodromies of the T-dualized defect HKT · 0.94
Cites as background 7 papers
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In this appendix, we briefly summarize the feature of defect five-branes discussed in [ref] .
Defect (p,q) Five-branes · Review of defect five-branes · 0.99
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The HKTs obtained by the conformal transformation have been studied in recent years from both mathematical and physical aspects [ref] .
Supersymmetric heterotic solutions via non-SU(3) standard embedding · Introduction · 0.90
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The HKTs obtained by the conformal transformation have been studied in recent years from both mathematical and physical aspects [ref] .
Heterotic warped Eguchi-Hanson spectra with five-branes and line bundles · Introduction · 0.90
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