I am trying to understand what is a Higgs bundle as defined in this paper by Gukov and Pei. They say it is a pair $(E, \Phi)$
$E$ is a holomorphic principal $G^\mathbb{C}$ bundle
$\Phi \in H^0(\Sigma, \mathrm{ad}(E) \otimes K )$
Can anyone explain to me a little about this sheaf $\mathrm{ad}(E) \otimes K$ ?