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

TL;DR

This paper demonstrates that 4-point correlators of 1/2-BPS operators in AdS$_2\times$S$^2$ can be computed using 4d conformal symmetry and an effective bulk action, revealing underlying higher-dimensional symmetries and their breaking by corrections.

Contribution

It adapts 10d conformal symmetry and effective field theory approaches from AdS$_5\times$S$^5$ to AdS$_2\times$S$^2$, analyzing correlators and higher derivative corrections.

Findings

4-point correlators can be computed using 4d conformal symmetry.

Higher derivative corrections involve Casimir operators and symmetry breaking.

Certain combinations of corrections preserve higher-dimensional symmetry at the integrand level.

Abstract

It was recently shown that IIB supergravity on AdS$_5\times$S$^5$ enjoys 10d conformal symmetry and that superstring theory on this background can be described using a 10d scalar effective field theory. In this paper we adapt these two complementary approaches to correlators of hypermultiplets in AdS$_2\times$S$^2$. In particular, we show that 4-point correlators of $1/2$-BPS operators in the 1d boundary can be computed using 4d conformal symmetry and a 4d effective action in the bulk. The 4d conformal symmetry is realised by acting with Casimirs of $SU(1,1|2)$, and is generically broken by higher 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 order Casimir acting on a 10d conformal block, similar structure does not appear in higher-order corrections. We note however that a specific combination of higher derivative corrections can give rise to Witten diagrams with higher dimensional symmetry at the integrand level, with breaking then arising from the measure.