Mirror Symmetric SU(3)-Structure Manifolds with NS Fluxes
By Stéphane Fidanza, R. Minasian, A. Tomasiello. 2003
137 citations recorded by the source corpus.
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 T3-fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (eiJ and Ω) 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.
Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/2ae1486ee34cfa1aed647dcc98242ce94db8e2f2
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Citations in the corpus
- T-duality, generalized geometry and non-geometric backgrounds (2008, methodology): “In the limit of vanishing B(2), we recover the results of [27], namely Φ+ and Φ− get exchanged under T-duality (if we write them in terms of dual vielbeins), and define a good mirror SU(3) structure.”
- Supersymmetric AdS(4) compactifications of IIA supergravity (2004, background): “There is already a considerable amount of literature on the subject, see [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34] for an inexhaustive list of references.”
- A scan for new N = 1 vacua on twisted tori (2006, methodology): “The intrinsic torsions for manifolds with SU(3) structure are differential forms Wi (to be reviewed shortly) in the representations 1, 8, 6, 6̄, 3, 3̄; the slogan in [61] was that 8 + 1↔ 6 + 3̄.”
- Generalized Complex Manifolds and Supersymmetry (2004, methodology): “Mirror symmetry as defined in [4] is inspired by T–duality along three directions.”
- SU(3) × SU(3) compactification and mirror duals of magnetic fluxes (2006, background): “We see that mirror symmetry requires the identification [12] Φ(M(6))↔ Φ(M̃(6)) , Φ(M(6))↔ Φ(M̃(6)) , (6.”
- Generalized N=1 orientifold compactifications and the Hitchin functionals (2006, background): “Evidence for this identification is provided by comparing the generalized type IIA and type IIB superpotentials.”
- A ten-dimensional action for non-geometric fluxes (2011, background): “Furthermore, it was quickly noticed that some non-geometric backgrounds can be obtained from string geometric backgrounds by applying T-dualities [15, 26], or equivalently [29] mirror symmetry [39, 40, 23].”
- New aspects of the dd c -lemma (2004, background): “Despite having been introduced only recently, generalized complex geometry is already being used to describe mirror symmetry at different levels in a growing number of papers [4, 31, 38, 59] and we will return to this topic at a later stage in this thesis.”
- Hitchin functionals in N = 2 supergravity (2005, background): “It was proposed in [23] that mirror symmetry for manifolds of SU(3) structure amounts to the exchange of the two pure spinors together with an exchange of even and odd RR-forms e−B−iJ ↔ Ω , Geven ↔ Godd .”
- Generalized complex geometry and T-duality (2011, background): “The action of T-duality on generalized complex structures was implicitly observed in [14], where both complex and symplectic structures in 6 dimensions were interpreted as spinors for CL(6, 6), a natural consideration from the point of view of supergravity.”
- Flux compactifications in string theory: A Comprehensive review (2005, methodology): “[121, 103, 153] perform three T-dualities along the fiber.”
- New aspects of the ddc-lemma (2005, unknown): “Despite having been introduced only recently, generalized complex geometry is already being used to describe mirror symmetry at different levels in a growing number of papers [4, 31, 38, 59] and we will return to this topic at a later stage in this thesis.”
- Supersymmetric backgrounds from generalized Calabi‐Yau manifolds (2004, methodology): “One is to go to the base, where one can define T–duality invariants, and further decompose the SU(3) representations 5The transformation rules for the fields as well as the working assumptions can be found in [4], here we just quote some relevant results.”