Hidden Conformal Symmetry in AdS $ _2\times $ S $^ 2$ Beyond Tree Level

摘要: Correlators of a certain one-dimensional superconformal field theory dual to hypermultiplets in AdSS exhibit a hidden four-dimensional conformal symmetry which allows one to repackage all tree-level 4-point correlators into a single four-dimensional object corresponding to a contact diagram arising from a massless theory in AdSS. This theory serves as a toy model for IIB string theory in AdSS and is interesting in its own right because AdSS describes the near-horizon limit of extremal black holes in four dimensions. We argue that after acting with an Casimir, all one-loop correlators can similarly be encoded by a four-dimensional function which arises from a one-loop scalar bubble diagram in AdSS, explaining how the hidden conformal symmetry extends beyond tree level. Finally, we conjecture a scalar effective field theory with a derivative interaction in AdSS whose Witten diagrams should directly reproduce 4-point correlators to all loops without acting with Casimirs.