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Understanding black hole entropy through the renormalization group

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It is known that the entanglement entropy of quantum
fields on the black hole
background contributes to the Bekenstein-Hawking entropy,and that its
divergences can be absorbed into the renormalization of gravitational
couplings. By introducing a Wilsonian cutoff scale and the concepts of
the renormalization group, we can expand this observation
into a broader framework for understanding black hole entropy. At a
given RG scale, two contributions to the black hole entropy can be
identified: the "gravitational" contribution coming from the
running effective gravitational action, and the entanglement entropy of the
quantum degrees of freedom below the cutoff scale. At different RG
scales the balance is different, though the total black hole entropy is
invariant. I will describe this picture for free fields,
considering both minimal and non-mininal coupling, and discuss the extension
to interacting fields and the difficulties it raises.