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Correlators of a certain one-dimensional superconformal field theory dual tohypermultiplets in AdS$_2\times$S$^2$ exhibit a hidden four-dimensionalconformal symmetry which allows one to repackage all tree-level 4-pointcorrelators into a single four-dimensional object corresponding to a contactdiagram arising from a massless $\phi^4$ theory in AdS$_2\times$S$^2$. Thistheory serves as a toy model for IIB string theory in AdS$_5\times$S$^5$ and isinteresting in its own right because AdS$_2\times$S$^2$ describes thenear-horizon limit of extremal black holes in four dimensions. We argue thatafter acting with an $SU(1,1)\times SU(2)$ Casimir, all one-loop correlatorscan similarly be encoded by a four-dimensional function which arises from aone-loop scalar bubble diagram in AdS$_2\times$S$^2$, explaining how the hiddenconformal symmetry extends beyond tree level. Finally, we conjecture a scalareffective field theory with a derivative interaction in AdS$_2\times$S$^2$whose Witten diagrams should directly reproduce 4-point correlators to allloops without acting with Casimirs.

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