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

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 ${\alpha }^{\prime }$ corrections to IIB supergravity in AdS${}_5\times$S${}^5$. In particular, while the ${\alpha }^{\prime 3}$ 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.

v2. published in JHEP

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Cited by in corpus (6)

• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Holographic S-fold theories at one loop
• All Next-to-Next-to-Extremal One-Loop Correlators of AdS Supergluons and Supergravitons
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Mellin amplitudes for $Ad{S}_3\times S^3$