Reference: Hwasung Lee, (2011). Strominger’s system on non-Kähler hermitian manifolds. DPhil. University of Oxford.Citable link to this page:
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 ��'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.
|Digital Origin:||Born digital|
|Type of Award:||DPhil|
|Level of Award:||Doctoral|
|Awarding Institution:||University of Oxford|
|Notes:||This thesis is not currently available via ORA.|