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It was recently shown that IIB supergravity on AdS$_5\times$S$^5$ enjoys 10dconformal symmetry and that superstring theory on this background can bedescribed using a 10d scalar effective field theory. In this paper we adaptthese two complementary approaches to correlators of hypermultiplets inAdS$_2\times$S$^2$. In particular, we show that 4-point correlators of$1/2$-BPS operators in the 1d boundary can be computed using 4d conformalsymmetry and a 4d effective action in the bulk. The 4d conformal symmetry isrealised by acting with Casimirs of $SU(1,1|2)$, and is generically broken byhigher derivative corrections. We point out similar structure underlying$\alpha'$ corrections to IIB supergravity in AdS$_5\times$S$^5$. In particular,while the $\alpha'^3$ corrections can be written in terms of a sixth orderCasimir acting on a 10d conformal block, similar structure does not appear inhigher-order corrections. We note however that a specific combination of higherderivative corrections can give rise to Witten diagrams with higher dimensionalsymmetry at the integrand level, with breaking then arising from the measure.

Higher-Dimensional Symmetry of AdS$_2\times$S$^2$ Correlators