I am trying to understand the basic construction in P. Biran's paper "Lagrangian Barriers and Symplectic Embeddings". At the begining (2.1), there is a construction which relies on the following things I would like some explanation or refference:
Suppose $(\Sigma,\tau)$ is a compact symplectic manifold and $L\rightarrow \Sigma$ a (complex) line bundle with $c_1(L)=[\tau]$. Pick any hermitian metric $h$ and define $E_L$ the unit disc bundle of $L$. Consider a connection $\nabla$ such that its curvature form is $R^{\nabla}=2\pi i\tau$. And $a^\nabla$ is the associated $\textit{transgression}$ $1$-form which satisfies certain properties.
My first question is this: Why can we find a connection with such an $R^\nabla$? My second question is: Can you provide me with a general refference of transgression forms.