Black hole entanglement entropy and the renormalization group

Abstract

We investigate the contributions of quantum fields to black hole entropy by using a cutoff scale at which the theory is described with a Wilsonian effective action. For both free and interacting fields, the total black hole entropy can be partitioned into a contribution derived from the gravitational effective action and a contribution from quantum fluctuations below the cutoff scale. In general the latter includes a quantum contribution to the Noether charge. We analyze whether it is appropriate to identify the rest with horizon entanglement entropy, and find several complications for this interpretation, which are especially problematic for interacting fields.

Superhorizon entanglement entropy from particle decay in inflation

“…The entanglement entropy has been the focus of several studies in condensed matter systems [52][53][54], 1 statistical physics and quantum field theory [56][57][58][59][60][61][62][63], black hole physics [64][65][66] and in particle production in time dependent backgrounds [67]. Most of these studies focus on entanglement between spatially correlated regions across boundaries.…”

Holographic RG flows, entanglement entropy and the sum rule

“…Susskind and Uglum proposed that entanglement entropy should renormalize in the same way as (4G N ) −1 [17]. The subject was revisited several times in the past [18][19][20][21][22][23][24][25].…”

“…Close to the AdS regions, the background equations of motion (2.7) give 21) and recalling the relation (2.9) between V and the AdS radius, obtains…”

Finite entanglement entropy in asymptotically safe quantum gravity

“…By adopting the discussion in [5] it is easy to see that (2.6) holds not only in flat space but also yields the leading scale dependence on curved classical spacetimes with any metricḡ αβ . Furthermore, equation (2.6) is equivalent to the RG equation discussed in [21] which employs a more general cutoff. (C) At this point we want to emphasize that in the EAA framework one usually regards the RG equations, requiring no UV cutoff, as having a more fundamental status than the functional integral from which they are derived in a formal way only.…”

“…Clearly, the physical interpretation of (1.4) is hampered by its UV divergence which cannot be "renormalized away" straightforwardly. Nevertheless, ever since its first discovery [6][7][8], the fact that S is proportional to the surface area rather than the volume of the subsystem traced over has sparked considerable interest and research activities [3,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. One of the reasons is clearly the similarity of (1.4) and the Bekenstein-Hawking entropy in black hole thermodynamics,…”