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john mangual
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representations of Higgs bundles

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 $\mathrm{ad}(E) \otimes K$ ?

john mangual
  • 22.8k
  • 4
  • 63
  • 172