Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds

Albrecht Klemm; Denis Klevers; Thomas W. Grimm

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Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds

Thomas W. Grimm, Albrecht Klemm, Denis Klevers

High Energy Physics - Theory · Submitted 29 Nov 2010

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The authors' main claim We argue that these deformations map to new complex structure deformations of a non-Calabi-Yau manifold which is obtained by blowing up the brane-curve into a four-cycle and by replacing the brane by background fluxes.

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arXiv ID1011.6375 (version 2)

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CitationAlbrecht Klemm, Denis Klevers, Thomas W. Grimm. "Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds." arXiv:1011.6375 (2010). https://pith.science/paper/DETEHA5Y

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We investigate the dynamics of space-time filling five-branes wrapped on curves in heterotic and orientifold Calabi-Yau compactifications. We first study the leading N=1 scalar potential on the infinite deformation space of the brane-curve around a supersymmetric configuration. The higher order potential is also determined by a brane superpotential which we compute for a subset of light deformations. We argue that these deformations map to new complex structure deformations of a non-Calabi-Yau manifold which is obtained by blowing up the brane-curve into a four-cycle and by replacing the brane by background fluxes. This translates the original brane-bulk system into a unifying geometrical formulation. Using this blow-up geometry we compute the complete set of open-closed Picard-Fuchs differential equations and identify the brane superpotential at special points in the field space for five-branes in toric Calabi-Yau hypersurfaces. This has an interpretation in open mirror symmetry and enables us to list compact disk instanton invariants. As a first step towards promoting the blow-up geometry to a supersymmetric heterotic background we propose a non-Kaehler SU(3) structure and an identification of the three-form flux.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the dynamics of space-time filling five-branes wrapped on curves in heterotic and orientifold Calabi-Yau compactifications.	contribution 0.72	0.83	0.04	asserted 0.91
s1	We first study the leading N=1 scalar potential on the infinite deformation space of the brane-curve around a supersymmetric configuration.	contribution 0.95	0.93	0.04	asserted 0.97
s2	The higher order potential is also determined by a brane superpotential which we compute for a subset of light deformations.	contribution 0.65	0.95	0.07	asserted 1.00
s3	We argue that these deformations map to new complex structure deformations of a non-Calabi-Yau manifold which is obtained by blowing up the brane-curve into a four-cycle and by replacing the brane by background fluxes.	interpretation 0.90	0.75	0.31	hedged possibility 0.45
s4	This translates the original brane-bulk system into a unifying geometrical formulation.	interpretation 0.96	0.59	0.16	asserted 0.99
s5	Using this blow-up geometry we compute the complete set of open-closed Picard-Fuchs differential equations and identify the brane superpotential at special points in the field space for five-branes in toric Calabi-Yau hypersurfaces.	contribution 0.49	0.95	0.18	asserted 1.00
s6	This has an interpretation in open mirror symmetry and enables us to list compact disk instanton invariants.	interpretation 0.91	0.88	0.10	asserted 0.99
s7	As a first step towards promoting the blow-up geometry to a supersymmetric heterotic background we propose a non-Kaehler SU(3) structure and an identification of the three-form flux.	future work 0.86	0.80	0.16	speculative 0.48

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.97.

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Original abstract

We investigate the dynamics of space-time filling five-branes wrapped on curves in heterotic and orientifold Calabi-Yau compactifications. We first study the leading N=1 scalar potential on the infinite deformation space of the brane-curve around a supersymmetric configuration. The higher order potential is also determined by a brane superpotential which we compute for a subset of light deformations. We argue that these deformations map to new complex structure deformations of a non-Calabi-Yau manifold which is obtained by blowing up the brane-curve into a four-cycle and by replacing the brane by background fluxes. This translates the original brane-bulk system into a unifying geometrical formulation. Using this blow-up geometry we compute the complete set of open-closed Picard-Fuchs differential equations and identify the brane superpotential at special points in the field space for five-branes in toric Calabi-Yau hypersurfaces. This has an interpretation in open mirror symmetry and enables us to list compact disk instanton invariants. As a first step towards promoting the blow-up geometry to a supersymmetric heterotic background we propose a non-Kaehler SU(3) structure and an identification of the three-form flux.

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Cited by 3 Pith papers

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

Landscaping with fluxes and the E8 Yukawa Point in F-theory
hep-th 2014-04 conditional novelty 7.0 of 10

An integral monodromy basis for Calabi-Yau fourfold periods is constructed and cross-checked, then used to argue that integer fluxes can drive F-theory moduli to orbifold and gauge-enhancement loci.
The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications
hep-th 2011-07 conditional novelty 6.0 of 10

Three computations of how a holomorphic vector bundle constrains the complex structure moduli of a Calabi-Yau threefold are argued to agree, and explicit bundles that freeze 80 of 82 moduli are exhibited.
Massive Abelian Gauge Symmetries and Fluxes in F-theory
hep-th 2011-07 conditional novelty 6.0 of 10

Massive Abelian gauge symmetries in F-theory arise from expanding the M-theory three-form on non-harmonic two-forms tied to non-Kahler resolutions, and fluxes along them reproduce known Type IIB tadpoles and chirality.

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18 arXiv papers cite this in 29 sentences

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Papers citing it · 15 sentences without a confident label

Builds on it 2 papers

Finally in section [ref] we extend, following [ref] , the reduction of [ref] to the full geometric deformation space of the D5-brane which is infinite dimensional and does include massive fields.

Holomorphic Couplings In Non-Perturbative String Compactifications · The Gauge Kinetic Function · 0.99
More precisely, $Ẑ_4$ is obtained as a non-Kähler resolution replacing [The explicit construction of $Ẑ_4$ should be the higher-dimensional generalization of the non-Kähler threefolds considered in [ref] .] Ŷ_4 → Ẑ_4 .

Massive Abelian Gauge Symmetries and Fluxes in F-theory · Non-harmonic forms for massive $U(1)$s · 0.95

Uses its method or tool 2 papers

A effective approach to obtain the D-brane superpotential is by using the blown-up geometry of target space along the submanifold wrapped by the D-branes [ref] .

Mirror Symmetry, D-brane Superpotential and Ooguri-Vafa Invariants of Compact Calabi-Yau Manifolds · Conclusion · 0.87
On the other hand, we will study these problems in this paper from an alternative approach [ref] that treats the complex structure deformations of the Calabi-Yau threefolds and the open string deformations of the D-branes on an equal footing by studying the complex structure deformations of a non-Calabi-Yau manifold obtained by blowing up the original Calabi-Yau threefold along curve wrapped by the D-brane.

D-brane Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds · Summary · 0.90

Uses its data or values 1 paper

As an explicit example of F-theory compactification, here we consider the background studied in [ref] (see also [ref] ), whose period integrals and topological intersection matrix are given by [equation] [equation] with the Euler characteristic $χ= 1860$.

F-theory Flux Vacua and Attractor Equations · Setup · 0.86

Compares with it 1 paper

However, in [ref] , they considered another approach which blows up along the curve C and replaces the pair(X,C) with a non-Calabi-Yau manifold $X$.

Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds with Three Deformations · Generalized GKZ system and Differential Operators · 0.85

Cites it as background 7 papers

Furthermore, there appeared some related works on superpotential for compact Calabi-Yau manifolds depending on open-closed deformation moduli [ref] . where the works [ref] studied it by the conformal field theory and matrix factorization and the others considered with Hodge theoretic method.

Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds with Three Deformations · Introduction · 0.84
Furthermore, there appeared some related works on superpotential for compact Calabi-Yau manifolds depending on open-closed deformation moduli [ref] . where the works [ref] studied it by the conformal field theory and matrix factorization, the works [ref] by the direct integration and the others considered with Hodge theoretic method.

D-brane Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds · Introduction · 0.88
They have in particular been used to address issues central to wall-crossing phenomena for BPS invariants for systems of D-branes [ref] , and to deriving a reliable index for microstate (quarter-BPS state) counting for single- and multi-centered black holes in $𝒩=4$ string theory [ref] (see also in the same line more mathematical works [ref] ).

Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms · Introduction · 0.87

What it cites · 99 sentences without a confident label

Builds on 1 paper

We straight forwardly extend the Kähler metric deduced in [ref] for the fields associated to $H^0(Σ,N_Z_3Σ)$ to the infinite dimensional space $𝒞^∞(Σ,N_Z_3Σ)$.

The D5-brane effective action and superpotential in N=1 compactifications · Calculation of the F-term Potential · 0.98

Uses the method or tool of 1 paper

Whenever we have a bulk integral over $Z_3$ we replace it by an integral over the open manifold $Z_3-Σ$ as [ref] [equation] where we substract a tubular neighborhood $𝒰_ϵ^(4)(Σ)$ of radius $ϵ$ over $Σ$.

Gravitational Anomaly Cancellation for M-Theory Fivebranes · Five-Branes in $𝒩=1$ Compactifications · 0.94

Compares with 9 papers

This agrees with the heterotic/F-theory dual fourfold when considering the elliptic $Z_3$ as a heterotic compactification [ref] .

Five-Brane Superpotentials and Heterotic/F-theory Duality · Toric Branes on $Z_3(1,1,1,6,9)$: the GKZ-System · 0.88
This can be compared to the method presented in [ref] where the obstructed deformations of a curve are identified with the unobstructed moduli of an appropriate divisor.

Mirror Symmetry for Toric Branes on Compact Hypersurfaces · Matching Deformations and Obstructions: Concrete Examples · 0.97
This can be compared to the method presented in [ref] where the obstructed deformations of a curve are identified with the unobstructed moduli of an appropriate divisor.

Effective superpotentials for compact D5-brane Calabi-Yau geometries · Matching Deformations and Obstructions: Concrete Examples · 0.97

Cites as background 22 papers

The non-closedness is parameterized by five torsion classes $_i$ which transform as $SU(3)$ irreducible representations [ref] .

The intrinsic torsion of SU(3) and G_2 structures · Brief Review on $SU(3)$ Structures and the Superpotential · 0.90
The non-closedness is parameterized by five torsion classes $_i$ which transform as $SU(3)$ irreducible representations [ref] .

Non-Kaehler String Backgrounds and their Five Torsion Classes · Brief Review on $SU(3)$ Structures and the Superpotential · 0.90
Flux compactifications provide a mechanism to give a mass to the deformations of the compactification manifold [ref] .

Les Houches Lectures on Constructing String Vacua · Introduction · 0.85

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