A QHE ' the effective action should be a local functional'

[binbagsss]

' Finally, if we care only about long distances, the effective action should be a local functional, meaning that we can write is as $S_{eff}[A]=\int d^d x...$ '

Where does this come from and what does it mean? This isn't at all familiar with me, and I don't recall ever seeing anything similar. Thanks.
http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf , page 145 David Tong notes QHE , chapter 5

 

[binbagsss]

' Finally, if we care only about long distances, the effective action should be a local functional, meaning that we can write is as $S_{eff}[A]=\int d^d x...$ '

Where does this come from and what does it mean? This isn't at all familiar with me, and I don't recall ever seeing anything similar. Thanks.
http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf , page 145 David Tong notes QHE , chapter 5

Also in his notes I see he uses $A \to A + \partial_{\mu}$ as a pose to $D_{\mu} \omega$, is this linked to the above? Is this sort of anagolous to GR where the 'connection vansihes' in this approximation or something - I make out the terms connection and potential are related from the notes but must differ somehow- in particular he later refers to $a_{\mu}$ as a connection as a pose to a potential (on the discussion of non-Albelian CS), the covaraint derivaitve I believe is defined to be the partial \pm i connection/potential ..I'm not sure exactly which formally, thanks