Abstract
We construct globally-defined SU(3) structures on smooth compact toric varieties (SCTV) in the class of \( \mathbb{C}{\mathrm{\mathbb{P}}}^1 \) bundles over M , where M is an arbitrary SCTV of complex dimension two. The construction can be extended to the case where the base is Kähler-Einstein of positive curvature, but not necessarily toric, and admits a parameter space which includes SU(3) structures of LT type.
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References
M. Larfors, D. Lüst and D. Tsimpis, Flux compactification on smooth, compact three-dimensional toric varieties, JHEP 07 (2010) 073 [arXiv:1005.2194] [INSPIRE].
M. Larfors, Revisiting toric SU(3) structures, Fortsch. Phys. 61 (2013) 1031 [arXiv:1309.2953] [INSPIRE].
M. Petrini and A. Zaffaroni, N = 2 solutions of massive type IIA and their Chern-Simons duals, JHEP 09 (2009) 107 [arXiv:0904.4915] [INSPIRE].
D. Lüst and D. Tsimpis, New supersymmetric AdS 4 type-II vacua, JHEP 09 (2009) 098 [arXiv:0906.2561] [INSPIRE].
G. Tian and S.-T. Yau, Kähler-Einstein metrics on complex surfaces with C(1) > 0, Commun. Math. Phys. 112 (1987) 175 [INSPIRE].
W. Fulton, Introduction to toric varieties, Annals of Mathematical Studies volume 131, Princeton University Press, Princeton, U.S.A. (1993).
F. Denef, Les Houches lectures on constructing string vacua, in the proceedings of the String theory and the real world: from particle physics to astrophysics, July 2-27, Les Houches, France (2007).
T. Oda, Torus embeddings and applications, Tata Inst. Fund. Res. Lectures on Math. and Phys. volume 58, Springer, Germany (1978).
J.P. Gauntlett, D. Martelli, J.F. Sparks and D. Waldram, A new infinite class of Sasaki-Einstein manifolds, Adv. Theor. Math. Phys. 8 (2004) 987 [hep-th/0403038] [INSPIRE].
D. Martelli and J. Sparks, Notes on toric Sasaki-Einstein seven-manifolds and AdS 4 /CF T 3, JHEP 11 (2008) 016 [arXiv:0808.0904] [INSPIRE].
D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [INSPIRE].
T. Friedrich and I. Kath, Einstein manifolds of dimension five with small first eigenvalue of the Dirac operator, J. Diff. Geom. 29 (1989) 263.
A. Tomasiello, New string vacua from twistor spaces, Phys. Rev. D 78 (2008) 046007 [arXiv:0712.1396] [INSPIRE].
P. Koerber, D. Lüst and D. Tsimpis, Type IIA AdS 4 compactifications on cosets, interpolations and domain walls, JHEP 07 (2008) 017 [arXiv:0804.0614] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].
F. Chen, K. Dasgupta, P. Franche, S. Katz and R. Tatar, Supersymmetric configurations, geometric transitions and new non-Kähler manifolds, Nucl. Phys. B 852 (2011) 553 [arXiv:1007.5316] [INSPIRE].
F. Xu, SU(3)-structures and special lagrangian geometries, math/0610532.
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ArXiv ePrint: 1707.04636
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Terrisse, R., Tsimpis, D. SU(3) structures on S2 bundles over four-manifolds. J. High Energ. Phys. 2017, 133 (2017). https://doi.org/10.1007/JHEP09(2017)133
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DOI: https://doi.org/10.1007/JHEP09(2017)133