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A companion to "Knot invariants and M-theory I'' [arXiv:1608.05128]: proofs and derivations
High Energy Physics - Theory · Submitted 23 Feb 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics.
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The abstract, sentence by sentence
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. We show that this theory has indeed all required properties to host knots. Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics. This is a companion paper to arXiv:1608.05128, covering all but section 3.3. It presents a detailed mathematical derivation of the main results there, as well as additional material. Among the new insights, those related to supersymmetry and the topological twist are highlighted. This paper offers an alternative, complementary formulation of the contents in~\cite{Dasgupta:2016rhc}, but is self-contained and can be read independently.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. | contribution 0.94 | 0.95 | 0.16 | asserted 1.00 |
| s1 | We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. | method 0.70 | 0.90 | 0.04 | asserted 0.77 |
| s2 | We show that this theory has indeed all required properties to host knots. | result 0.97 | 0.91 | 0.25 | asserted 1.00 |
| s3 | Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics. | interpretation 0.75 | 0.86 | 0.29 | asserted 1.00 |
| s4 | This is a companion paper to arXiv:1608.05128, covering all but section 3.3. | background 0.56 | 0.42 | 0.03 | asserted 1.00 |
| s5 | It presents a detailed mathematical derivation of the main results there, as well as additional material. | contribution 0.95 | 0.92 | 0.07 | asserted 1.00 |
| s6 | Among the new insights, those related to supersymmetry and the topological twist are highlighted. | contribution 0.95 | 0.76 | 0.06 | asserted 0.85 |
| s7 | This paper offers an alternative, complementary formulation of the contents in~\cite{Dasgupta:2016rhc}, but is self-contained and can be read independently. | contribution 0.81 | 0.61 | 0.11 | asserted 1.00 |
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The paper
Original abstract
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory models. We show that this theory has indeed all required properties to host knots. Our analysis provides a unifying picture of the various recent works that attempt an understanding of knot invariants using techniques of four-dimensional physics. This is a companion paper to arXiv:1608.05128, covering all but section 3.3. It presents a detailed mathematical derivation of the main results there, as well as additional material. Among the new insights, those related to supersymmetry and the topological twist are highlighted. This paper offers an alternative, complementary formulation of the contents in~\cite{Dasgupta:2016rhc}, but is self-contained and can be read independently.
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How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 155 sentences without a confident label
Builds on 1 paper
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Right afterwards, it is generalized to ([ref]), a novel result from the perspective of [ref] .
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators · Relation between the present work and CITEMARK13Z · 0.83
Uses the method or tool of 6 papers
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Following equation (4.3) in [ref] , we define the quantity [equation] Using the above two equations in $ds_(M,3)^2$, it is a matter of simple algebra to check that the boosted M-theory metric is given by [equation] Note that the boost has now generated a gauge field in the M-theory.
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators · Obtaining a type IIB configuration with RR and NS fluxes: a boost in M-theory · 0.86
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However, the series of dualities first presented in [ref] and later on further studied in [ref] and [ref] , when applied to our above configuration, precisely serves this purpose.
Non-Kahler Resolved Conifold, Localized Fluxes in M-Theory and Supersymmetry · Demanding $𝒩=1$ supersymmetry: torsion classes · 0.94
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However, the series of dualities first presented in [ref] and later on further studied in [ref] and [ref] , when applied to our above configuration, precisely serves this purpose.
The unwarped, resolved, deformed conifold: fivebranes and the baryonic branch of the Klebanov-Strassler theory · Demanding $𝒩=1$ supersymmetry: torsion classes · 0.94
Compares with 3 papers
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The geometry and fluxes of this final type IIB configuration are precisely those in (4.2) in [ref] .
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators · Obtaining a type IIB configuration with RR and NS fluxes: a boost in M-theory · 0.86
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Focusing on the case where (M, 1) is indeed $𝒰$-invariant, we can precisely reproduce the results in [ref] .
Fivebranes and Knots · Ensuring maximally supersymmetric boundary conditions · 0.93
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We shall introduce the concept of topological twist and twist our own theory in due time, in section [ref].] in [ref] and [ref] .
Knot Invariants from Four-Dimensional Gauge Theory · Consistency requirements and advantage of rewriting ([ref]) as ([ref]) · 0.92
Cites as support 1 paper
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The argument between (3.91) and (3.98) in [ref] in terms of a sigma model may well be the most solid evidence for this claim.
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators · Kinetic term of the G-flux · 0.99
Cites as background 9 papers
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Starting roughly at the same time and up to now, there have been a number of works that address the study of knot invariants from the point of view of four-dimensional physics: [ref] , to mention a few.
Surface Operators and Knot Homologies · Introduction · 0.96
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Starting roughly at the same time and up to now, there have been a number of works that address the study of knot invariants from the point of view of four-dimensional physics: [ref] , to mention a few.
Fivebranes and Knots · Introduction · 0.96
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Starting roughly at the same time and up to now, there have been a number of works that address the study of knot invariants from the point of view of four-dimensional physics: [ref] , to mention a few.
Knot Invariants from Four-Dimensional Gauge Theory · Introduction · 0.96
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