Mirror symmetric SU(3)-structure manifolds with NS fluxes

Alessandro Tomasiello; Ruben Minasian; Stephane Fidanza

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Mirror symmetric SU(3)-structure manifolds with NS fluxes

Stephane Fidanza, Ruben Minasian, Alessandro Tomasiello

High Energy Physics - Theory · Submitted 14 Nov 2003

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

The authors' main claim When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side.

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arXiv IDhep-th/0311122 (version 1)

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CitationAlessandro Tomasiello, Ruben Minasian, Stephane Fidanza. "Mirror symmetric SU(3)-structure manifolds with NS fluxes." arXiv:hep-th/0311122 (2003). https://pith.science/paper/T4EQCMBH

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When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side. Considering a general class of T^3-fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (e^{iJ} and \Omega) in dual geometries under fiberwise T-duality, and study the transformations of the NS flux and the components of intrinsic torsion. A complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with NS 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	When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side.	background 0.97	0.14	0.58	asserted 1.00
s1	Considering a general class of T^3-fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (e^{iJ} and \Omega) in dual geometries under fiberwise T-duality, and study the transformations of the NS flux and the components of intrinsic torsion.	result 0.53	0.95	0.27	asserted 1.00
s2	A complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with NS flux.	contribution 0.80	0.89	0.38	asserted 0.64

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Original abstract

When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side. Considering a general class of T^3-fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (e^{iJ} and \Omega) in dual geometries under fiberwise T-duality, and study the transformations of the NS flux and the components of intrinsic torsion. A complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with NS flux.

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References

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Cited by 18 Pith papers

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The paper derives N=1 Kähler potentials and superpotentials for type II orientifolds on SU(3)-structure manifolds and proposes generalized half-flat manifolds as mirrors of Calabi-Yau compactifications with NS-NS flux.
Nongeometric Flux Compactifications
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Generalized structures of N=1 vacua
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N=1 type II vacua with Ramond-Ramond flux are characterized by two pure spinor equations: one requires a twisted generalized Calabi-Yau, the other sources the second spinor with the RR field.

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For G2 and SU(3) string backgrounds with NS flux, the scalar torsion class controls the first-order deformation of the worldsheet super W-algebra couplings away from special holonomy.
Non-Geometric Fluxes in Supergravity and Double Field Theory
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T-duality, Generalized Geometry and Non-Geometric Backgrounds
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T-duality is realized as an O(d,d) rotation of generalized vielbeins and pure spinors, and the four-dimensional fluxes f, H, Q, R are identified with Courant-bracket structure constants of those vielbeins.
A scan for new N=1 vacua on twisted tori
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The paper classifies N=1 Minkowski vacua of type II strings on compact nilmanifolds and solvmanifolds, finding a few new non-Calabi-Yau backgrounds that so far exist only as smeared large-volume solutions.
Twisted tori and fluxes: a no go theorem for Lie groups of weak G_2 holonomy
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No seven-dimensional Lie group admits weak G2 holonomy, so no unwarped, source-free M-theory compactification of the form AdS4 times a group manifold with nontrivial internal flux exists.
Supersymmetric D-branes and calibrations on general N=1 backgrounds
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Supersymmetric D-branes in general N=1 flux backgrounds wrap generalized complex submanifolds and are calibrated by a form built from the non-integrable pure spinor plus the Ramond-Ramond potentials.
Hitchin Functionals in N=2 Supergravity
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Type II supergravity on SU(3) x SU(3)-structure backgrounds admits a special Kähler geometry on its metric moduli space, with Kähler potentials given by Hitchin functionals, and its gravitino transformations yield N=2...
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N=1 supersymmetric AdS4 compactifications of massive IIA supergravity require a half-flat internal six-manifold with torsion in two specific classes, and all form fluxes are fixed by the internal geometry.
A ten-dimensional action for non-geometric fluxes
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A change of field variables recasts the ten-dimensional NSNS Lagrangian so that the non-geometric Q-flux appears explicitly, and dimensional reduction reproduces the known four-dimensional Q-flux potential.
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T-duality between torus bundles with 3-form flux is an isomorphism of Courant algebroids, which transports Dirac, generalized complex, generalized metric and generalized Kähler structures between the two spaces.
Flux compactifications in string theory: a comprehensive review
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14 arXiv papers cite this in 17 sentences

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Compares with it 1 paper

Then one can show that (taking the initial $B_αβ=0$ for simplicity) the Buscher rules for this element can be summarized by acting on ([ref]) by the simple rules [equation] this result is very similar to the one in [ref] for the simpler inversion along the three direction of the fibre.

Generalized Kaehler Potentials from Supergravity · T–duality and bivector action · 0.97

Cites it as background 6 papers

U-folds are consistent backgrounds that incorporate in a non-trivial manner the natural symmetries of a supergravity or string theory [ref] .

Geometric U-folds in four dimensions · Introduction and main results · 0.99
The SYZ [ref] approach is well motivated from the target space physics and it seems promising that this can be generalized to flux backgrounds [ref] but this is difficult to check even in Calabi-Yau examples.

Missing Mirrors: Type IIA Supergravity on the Resolved Conifold · Introduction · 0.93
Restricting to three-folds, there has been considerable interest in extending mirror symmetry to include $3$-structure manifolds with torsion [ref] .

All-orders moduli for type II flux backgrounds · Conclusions · 0.96

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