Mirror symmetry in generalized Calabi–Yau compactifications ☆

By Sébastien Gurrieri, J. Louis, Andrei Micu, D. Waldram. 2002

390 citations recorded by the source corpus.

Abstract We discuss mirror symmetry in generalized Calabi–Yau compactifications of type II string theories with background NS-fluxes. Starting from type IIB compactified on Calabi–Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class of six-manifolds. These mirror manifolds have SU (3) structure and are termed half-flat ; they are neither complex nor Ricci-flat and their holonomy group is no longer SU (3). We show that type IIA appropriately compactified on such manifolds gives the correct mirror-symmetric low-energy effective action.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/66f8cd8bfa930d19fc00e8825d876698047b1375

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. M. Graña
2. J. Sparks
3. D. Martelli
4. D. Waldram
5. Paul Koerber
6. A. Tomasiello
7. Shing-Tung Yau
8. E. Witten

In Nuclear and High Energy Physics

1. M. Graña
2. D. Lust
3. Ralph Blumenhagen
4. Eran Palti
5. Thomas W. Grimm
6. D. Waldram
7. A. Uranga
8. J. Louis

Citations in the corpus

• The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets (2008, background): “In generic flux compactifications, the set of harmonic forms would be unsuitable as expansion forms, as the forms J and that define the SU(3)-structure (and which enter the supergravity expressions for the K¨ahler and superpotential) are no longer closed (see e.g. [ 37 , 30, 34] for a few proposals)”
• Non‐geometric fluxes in supergravity and double field theory (2012, background): “For elliptically fibered Calabi–Yau manifolds, mirror symmetry reduces to T-duality [72], and it is possible that the field redefinition we propose is useful for the study of their non-geometric duals [9, 79,80].”
• Compactifications of heterotic strings on non-Kähler complex manifolds II (2003, background): “Since all these details have already appeared in [70],[71],[56]we will not repeat them here.”
• Counting flux vacua (2003, background): “They went on to argue that the number of flux vacua should go as Nvac ∼ L , where K is the number of cycles supporting flux, and L is an “average number 2 While there is a larger T-duality group, it does not identify Calabi-Yau compactifications, but produces new, non-Kähler compactifications [29,24”
• Superstrings with intrinsic torsion (2003, background): “Similar ideas have been used to analyse other supergravity solutions in [12, 13, 14, 15, 16].”
• A scan for new N = 1 vacua on twisted tori (2006, background): “The appearance of half–flat geometries looks curious in light of their role as mirrors of Calabi–Yau’s with H flux [77]; this allows for an explicit construction of half–flat manifolds starting from CY geometry [78].”
• Flux compactifications in string theory: A Comprehensive review (2005, background): “[121] made precise the conjecture in Ref.”
• Gauged Supergravities. (2016, methodology): “The general features of the four-dimensional supergravity were derived within a top-down approach, using generalized geometry, in [107], building on previous related works, see [304, 305] and references therein.”
• G structures, fluxes and calibrations in M theory (2003, methodology): “Subsequent works have used this approach to analyse and classify supersymmetric backgrounds in various supergravity theories [2, 3, 4, 5, 6, 7, 8, 9, 10].”
• M-theory, exceptional generalised geometry and superpotentials (2008, background): “This description has proved very useful in, among other things: characterising supersymmetric backgrounds, finding new examples with non-zero fluxes and writing supersymmetric low-energy effective theories [5]–[25]; describing topological string theories and generic N = (2, 2) σ-models [26]–[39]; as”
• Generalized complex geometry and T-duality (2011, background): “Once the connection with generalized geometry was understood, several works appeared [16, 19, 12, 23, 24, 29, 28] which provide a physical motivation and justification for the use of generalized complex structures to understand mirror symmetry.”