Hidden Conformal Symmetry in AdS2×S2 Beyond Tree Level
Abstract
Correlators of a certain one-dimensional superconformal field theory dual to hypermultiplets in AdS2×S2 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 φ4 theory in AdS2×S2. This theory serves as a toy model for IIB string theory in AdS5×S5 and is interesting in its own right because AdS2×S2 describes the near-horizon limit of extremal black holes in four dimensions. We argue that after acting with an SU(1,1)× SU(2) Casimir, all one-loop correlators can similarly be encoded by a four-dimensional function which arises from a one-loop scalar bubble diagram in AdS2×S2, explaining how the hidden conformal symmetry extends beyond tree level. Finally, we conjecture a scalar effective field theory with a derivative interaction in AdS2×S2 whose Witten diagrams should directly reproduce 4-point correlators to all loops without acting with Casimirs.
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