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No description available.

In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³). We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08]. Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.

Davis and Januszkiewicz introduced in 1981 a family of compact real manifolds, the Quasi-Toric Manifolds, with a group action by a torus, a direct product of circle (T) groups. Their manifolds have an orbit space which is a simple polytope with a distinct isotropy subgroup associated to each face of the polytope, subject to some consistency conditions. They defined a characteristic function which captured the properties of the isotropy subgroups, and showed that their manifolds can be classified by the polytope and characteristic function. They further showed that the cohomology ring of the manifold can be written down directly from properties derived from the polytope and the characteristic function. This work considers the question of how far the circle group T can be replaced by the group of unit quaternions Q in the construction and description of quasi-toric manifolds. Unlike T, the group Q is not commutative, so the actions of Q n on the product H n of the set of quaternions using quaternionic multiplication are studied in detail. Then, in direct analogy to the quasi-toric manifolds, a family of compact real manifolds, the Quoric Manifolds, is introduced which have an action by Q n, and whose orbit space is a polytope. A characteristic functor is defined on the faces of the polytope which captures the properties of the isotropy classes of the orbits of the action. It is shown that quoric manifolds can be classified in a manner similar to the quasi-toric manifolds, by the polytope and characteristic functor. A restricted family, the global quoric manifolds, which satisfy an additional condition are defined. It is shown that an infinite number of polytopes exist in any dimension over which a global quoric manifold can be defined. It is shown that any global quoric manifold can be described as a quotient space of a moment angle complex over the polytope, and that its integral cohomology ring can be calculated, taking a form analagous to that in the quasi-toric case.

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