Abstract
We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial T4 fibrations over Calabi–Yau two-folds. These give rise to eight-dimensional non-Kähler Hermitian manifolds with SU(4) structure. The eight-manifold is also a circle fibration over a seven-dimensional G2 manifold with skew torsion. The eight-manifolds of this type appear as internal manifolds with SU(4) structure in type IIB string theory with F3 and F7 fluxes. These manifolds have generalized calibrated cycles in the presence of fluxes.
Highlights
String theory has elegant and deep mathematical structures
A natural question that is addressed by this present paper is what happens if we use T 4 fibrations, instead of T 2 fibrations. This corresponds to a geometric model of eightdimensional manifolds that we construct in this paper
The geometric model of T 4 fibrations over Calabi-Yau two-folds constructed in this paper provides examples of eight-dimensional balanced manifolds and non-Kahler Hermitian manifolds
Summary
String theory has elegant and deep mathematical structures. It relates theoretical physics to mathematics and has provided great insights to both areas of research. An interesting model of manifolds with SU(3) structure, is the geometric construction of T 2 fibrations over Calabi-Yau two-folds [1, 2]. Such six-dimensional manifolds include Calabi-Yau three-folds of the Kahler type, and non-Kahler Hermitian manifolds with SU(3) structure They can appear as the internal six-manifolds when the superstring theory is compactified down to four-dimensional spacetime. In the compactification of heterotic string theory to four dimensional Minkowski spacetime [6], the internal six-manifolds can become non-Kahler in the presence of fluxes [7, 8, 1, 9]. We will construct eight-dimensional manifolds of the non-Kahler Hermitian type, by T 4 fibrations over Calabi-Yau two-folds.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
