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Supersymmetric Configurations, Geometric Transitions and New Non-Kahler Manifolds
High Energy Physics - Theory · Submitted 29 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.
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The abstract, sentence by sentence
We give a detailed derivation of a supersymmetric configuration of wrapped D5-branes on a two-cycle of a warped resolved conifold. Our analysis reveals that the resolved conifold should support a non-Kahler metric with an SU(3) structure. We use this as a starting point of the geometric transition in type IIB theory. A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G_2 structure, gives rise to the complete IR geometric transition in type IIA theory. A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5-branes. Expectedly non-Kahler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. In the local limit we reproduce precisely the scenarios presented in our earlier works. Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We give a detailed derivation of a supersymmetric configuration of wrapped D5-branes on a two-cycle of a warped resolved conifold. | contribution 0.97 | 0.96 | 0.07 | asserted 1.00 |
| s1 | Our analysis reveals that the resolved conifold should support a non-Kahler metric with an SU(3) structure. | result 0.96 | 0.92 | 0.32 | asserted 0.82 |
| s2 | We use this as a starting point of the geometric transition in type IIB theory. | method 0.89 | 0.75 | 0.05 | asserted 0.98 |
| s3 | A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G_2 structure, gives rise to the complete IR geometric transition in type IIA theory. | method 0.74 | 0.75 | 0.13 | asserted 1.00 |
| s4 | A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5-branes. | result 0.71 | 0.78 | 0.11 | asserted 1.00 |
| s5 | Expectedly non-Kahler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. | interpretation 0.54 | 0.55 | 0.34 | hedged possibility 0.74 |
| s6 | In the local limit we reproduce precisely the scenarios presented in our earlier works. | result 0.91 | 0.82 | 0.06 | asserted 1.00 |
| s7 | Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories. | interpretation 0.94 | 0.75 | 0.75 | asserted 0.69 |
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The paper
Original abstract
We give a detailed derivation of a supersymmetric configuration of wrapped D5-branes on a two-cycle of a warped resolved conifold. Our analysis reveals that the resolved conifold should support a non-Kahler metric with an SU(3) structure. We use this as a starting point of the geometric transition in type IIB theory. A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G_2 structure, gives rise to the complete IR geometric transition in type IIA theory. A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5-branes. Expectedly non-Kahler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. In the local limit we reproduce precisely the scenarios presented in our earlier works. Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.
Human review
How the literature uses it
21 arXiv papers cite this in 103 sentences
Papers citing it · 76 sentences without a confident label
Contests it 1 paper
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Naively, this can be obtained by performing three T-dualities along $ψ$, $ϕ_1$, and $ϕ_2$, but this would lead to an erroneous result [ref] .
Gauge/Gravity Duality in Heterotic String Theory · Type I$^'$ and type IIA duality frames · contest 0.72
Builds on it 1 paper
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The work in this paper is a direct followup of our last paper [ref] where various supersymmetric duals in type II and M-theory were presented in the geometric transition set-up.
Toward the Gravity Dual of Heterotic Small Instantons · Introduction · 0.95
Uses its method or tool 8 papers
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Following the steps and notation in [ref] , we find the metric: ds^2_IIA = e^-ϕ[ds^2_0123 + H_2 dr^2] + H_1(dψ+ Δ_1 cosθ_1 dϕ_1 + Δ_2 cosθ_2 dϕ_2)^2 + (H_3a dθ_1^2 + H_3bdϕ_2^2) + (H_4a dθ_2^2 + H_4bdϕ_1^2)where $ϕ$ is the remnant of the dilaton factor from M-theory after flop and $H_2$ is the same as in [ref].
Gauge/Gravity Duality in Heterotic String Theory · Gravity duals in the heterotic theories · 0.93
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The steps for creating a supersymmetric wrapped D5 brane with three-form fluxes now follow the trick laid out by [ref] .
Non-Kahler Resolved Conifold, Localized Fluxes in M-Theory and Supersymmetry · D5-branes on a Non-Kähler Resolved Conifold · 1.00
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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.
A companion to "Knot invariants and M-theory I'' [arXiv:1608.05128]: proofs and derivations · Demanding $𝒩=1$ supersymmetry: torsion classes · 0.94
Uses its data or values 1 paper
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For the other coefficients, one may look up their values in section 4.4 of [ref] .[Note that one has to set to zero all of the $b_ij$ fields that appear in the fibrational structure in [ref] .] The various components of the fluxes could be traced from the original type I side or from [ref] and [ref].
Gauge/Gravity Duality in Heterotic String Theory · Gravity duals in the heterotic theories · 0.81
Compares with it 4 papers
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Compared to some of our earlier works [ref] , this is a more direct way to integrate these theories into a single duality chain.
Gauge/Gravity Duality in Heterotic String Theory · Introduction · 0.93
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The constructions of [ref] share sensible similarities with our approach.
Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds · The $SU(3)$ Structure on the Manifold $Ẑ_3$ · 0.91
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A somewhat similar picture was recently proposed in a slightly different scenario involving $N = 1$ dualities in the heterotic side in [ref] .
F-Theory, Seiberg-Witten Curves and N = 2 Dualities · F-theory/heterotic dualities and a supergravity picture · 0.84
Cites it as support 3 papers
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As discussed in [ref] , the metric on the resolved conifold has to be non-Kähler to satisfy all the EOMs and supersymmetry.
Non-Kahler Resolved Conifold, Localized Fluxes in M-Theory and Supersymmetry · Introduction · 0.98
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This choice does not change the local NS three-form flux, as was shown in [ref] .
Bulk Viscosity at Extreme Limits: From Kinetic Theory to Strings · The mirror type IIA model and its M-theory uplift · 0.99
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However despite this obstacle, one thing is clear from the analysis of [ref] : the resultant metric will not be a Kähler manifold, in fact, it may not even be a complex manifold.
On the Scalar Spectrum of the Y^{p,q} Manifolds · Resolution and deformation of the cones over $Y^p,q$ · 0.97
Cites it as background 3 papers
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Nevertheless, some recent progress has been made in a series of papers [ref] , as well as [ref] , starting with the program initiated in [ref] .
Gauge/Gravity Duality in Heterotic String Theory · Introduction · 0.91
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For details the readers may refer to [ref] .
Non-Kahler Resolved Conifold, Localized Fluxes in M-Theory and Supersymmetry · M-theory Lift of the Five-brane on a Warped Resolved Conifold · 0.91
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For a sampling of literature, see [ref] .
Linear Sigma Models with Torsion · Introduction · 1.00
What it cites · 109 sentences without a confident label
Contests 4 papers
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It turns out however that the mirror rules of [ref] , as discussed in [ref] , do not quite suffice.
Mirror Symmetry is T-Duality · Geometric transition and supersymmetric solution · contest 0.78
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It turns out however that the mirror rules of [ref] , as discussed in [ref] , do not quite suffice.
Geometric Transitions, Flops and Non-Kahler Manifolds: I · Geometric transition and supersymmetric solution · contest 0.78
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We can, however, not use the metric for D5 branes wrapping the $S^2$ of a resolved conifold as derived in [ref] , because it breaks all supersymmetry [ref] .
3-branes on resolved conifold · Geometric transition and supersymmetric solution · contest 0.86
Builds on 1 paper
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Let us see how from our local picture studied in [ref] these two possibilities can be realised.
Geometric Transitions, Flops and Non-Kahler Manifolds: I · Analysis of the global picture in type IIB · 0.84
Uses the method or tool of 5 papers
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Following the first paper of [ref] we first express the B-fields appearing in the fibration [ref] in terms of periodic angular coordinates $λ_i$ in the following way: [equation] Using these we can define two sets of one-forms.
Geometric Transitions, Flops and Non-Kahler Manifolds: I · M theory lift, flop transition and type IIA reduction · 0.98
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Due to the global nature of our metric, the operation of flop can be performed by a class of transformations parametrized by the values of $a$, $b$ etc. in the following way: [equation] Now comparing [ref] and [ref] one can pretty much fix the coefficients $c, d$ etc. in terms of $a, b$ in the following way: c=a√(k^2G_2+kG_3+G_1/ω^2G_5+ωG_6+G_4), d=b√(μ^2G_2+μG_3+G_1/τ^2G_5+τG_6+G_4) e=ak, g=cω, f=bμ, h=dτwhere $a, b$ can in turn be fixed by computing the $G_2$-torsion classes and demanding supersymmetry (see also [ref] ).
Toward the Gravity Dual of Heterotic Small Instantons · M theory lift, flop transition and type IIA reduction · 0.87
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We follow [ref] which gives a general procedure for constructing string compactifications on toric varieties via a method for producing $SU(3)$ structures.
Flux compactification on smooth, compact three-dimensional toric varieties · $SU(3)$ structure · 1.00
Compares with 8 papers
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(6.3) in the first paper of [ref] .
Geometric Transitions, Flops and Non-Kahler Manifolds: I · M theory lift, flop transition and type IIA reduction · 0.91
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The metric that we proposed in [ref] (where we kept the harmonic functions undetermined) is very close to the metric of [ref] but differs in some subtle way:
3-branes on resolved conifold · Geometric transition and supersymmetric solution · 0.95
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The configuration that we have is exactly opposite of the case [ref] .
Mirror Symmetry is T-Duality · Geometric transition and supersymmetric solution · 0.80
Cites as support 3 papers
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Other possible cross-terms, not considered in [ref], will only make the IIA background more non-trivial without revealing new physics[We have justified this claim in [ref] where we explicitly computed the torsion classes for the background [ref], [ref] and [ref] to argue for supersymmetry.
Toward the Gravity Dual of Heterotic Small Instantons · More explicit type IIB background before geometric transition · 0.97
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The replacement of spheres by two tori was directly motivated from the corresponding brane constructions of [ref] , where non-compact NS5 branes required the existence of tori instead of spheres in the T-dual picture.
Brane Configurations for Branes at Conifolds · Analysis of the global picture in type IIB · 0.96
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This is consistent with the prediction of [ref] .
Evidence for F-Theory · Geometric transition and supersymmetric solution · 0.97
Cites as background 8 papers
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For more details see [ref] .
Geometric Transitions, Flops and Non-Kahler Manifolds: I · Analysis of the global picture in type IIB · 0.81
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The first kind of dualities that consider the actual running of the coupling constants leading to, say, confining theories were discussed some time back in [ref] , [ref] , [ref] and its extension to include fundamental flavors in [ref] .
Superstrings and Topological Strings at Large N · Introduction · 0.95
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The first kind of dualities that consider the actual running of the coupling constants leading to, say, confining theories were discussed some time back in [ref] , [ref] , [ref] and its extension to include fundamental flavors in [ref] .
Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities · Introduction · 0.95
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