‘Hetu’-‘Luoshu’'s laws of changes and Ilbu' ‘Right Change’

One-Loop Test of Quantum Black Holes in anti–de Sitter Space

“…Our precise example, when taken in conjunction with [7] and [10], clarifies that the quantum entropy function that has been so successful in the context of asymptotically flat black holes needs to be revisited in the context of asymptotically AdS black holes. Arguably, the connection between degrees of freedom residing at the horizon and other potential hair degrees of freedom needs to be better understood by revisiting previous approaches [29,30].…”

“…In our previous work we studied corrections to the topologically twisted index using a combination of numerical and analytical techniques and identified a logarithmic correction of the form − 1 2 log N [7]. A corresponding computation on the gravity side, focusing on the near horizon contribution to the one-loop effective action and following the quantum entropy formalism developed by Sen [8,9], however, failed to match this microscopic result [7,10]. However, here we report that perfect agreement is achieved when the one-loop supergravity computation is performed in the full AdS 4 black hole background, and not just in the near horizon geometry.…”

“…The standard computation of such terms for black holes in asymptotically flat spacetime reduces to the near horizon geometry [9]. However, in [7,10], the near horizon contribution was shown to be −2 log N , resulting in a mismatch with the field theory answer. Such a mismatch indicates that either somehow the near horizon geometry is not enough to compute the quantum entropy, or the index does not correctly count microstates in the sub-leading order.…”