Journal of High Energy Physics

, 2019:171 | Cite as

Calabi-Yau manifolds and SU(3) structure

  • Magdalena LarforsEmail author
  • Andre Lukas
  • Fabian Ruehle
Open Access
Regular Article - Theoretical Physics


We show that non-trivial SU(3) structures can be constructed on large classes of Calabi-Yau three-folds. Specifically, we focus on Calabi-Yau three-folds constructed as complete intersections in products of projective spaces, although we expect similar methods to apply to other constructions and also to Calabi-Yau four-folds. Among the wide range of possible SU(3) structures we find Strominger-Hull systems, suitable for heterotic or type II string compactifications, on all complete intersection Calabi-Yau manifolds. These SU(3) structures of Strominger-Hull type have a non-vanishing and non-closed three-form flux which needs to be supported by source terms in the associated Bianchi identity. We discuss the possibility of finding such source terms and present first steps towards their explicit construction. Provided suitable sources exist, our methods lead to Calabi-Yau compactifications of string theory with a non Ricci-flat, physical metric which can be written down explicitly and in analytic form.


Flux compactifications Superstring Vacua Superstrings and Heterotic Strings 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUppsala UniversityUppsalaSweden
  2. 2.Rudolf Peierls Centre for Theoretical PhysicsUniversity of OxfordOxfordU.K.

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