Abstract
It was recently shown that IIB supergravity on AdS5×S5 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 AdS2×S2. 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 α′ corrections to IIB supergravity in AdS5×S5. In particular, while the α′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.
Highlights
Understanding quantum field theory and quantum gravity in curved backgrounds such as black holes and cosmological spacetimes is one of the most pressing questions in theoretical physics
The second approach we develop is based on a 4d scalar effective action analogous to the 10d effective action for IIB string theory in AdS5×S5 [13]
One can compute generalised Witten diagrams which treat AdS and S on equal footing, giving a whole tower of 4-point correlators corresponding to harmonics on the sphere
Summary
Understanding quantum field theory and quantum gravity in curved backgrounds such as black holes and cosmological spacetimes is one of the most pressing questions in theoretical physics. Subsequent work showed that 10d conformal symmetry is broken by string corrections [12] In another development, a simple 10d scalar effective action was conjectured to describe all 4-point correlators of 1/2-BPS operators in N = 4 SYM dual to tree-level string theory in AdS5× S5 to all orders in α [13]. We find that only a special infinite class of correlators derived from the effective action with higher derivative corrections can be reproduced by acting with Casimirs on 4d conformal blocks, suggesting that 4d conformal symmetry is generically broken by higher derivative corrections This is further confirmed by the structure of anomalous dimensions of double trace operators which we compute using a procedure for unmixing operators which are degenerate at leading order in the central charge expansion reminiscent of [24]. We have a number of appendices providing more details about superconformal Casimirs, correlators of descendent operators, and further examples of unmixing
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