We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries.
We provide strong evidence that all tree-level 4-point holographic correlators in $$\hbox {AdS}_3 \times S^3$$AdS3×S3 are constrained by a hidden 6D conformal symmetry. This property has been discovered in the $$\hbox {AdS}_5 \times S^5$$AdS5×S5 context and noticed in the tensor multiplet subsector of the AdS$$_3 \times S^3$$3×S3 theory. Here we extend it to general AdS$$_3 \times S^3$$3×S3 correlators which contain also the chiral primary operators of spin zero and one that sit in the gravity multiplet. The key observation is that the 6D conformal primary field associated with these operators is not a scalar but a self-dual 3-form primary. As an example, we focus on the correlators involving two fields in the tensor multiplets and two in the gravity multiplet and show that all such correlators are encoded in a conformal 6D correlator between two scalars and two self-dual 3-forms, which is determined by three functions of the cross ratios. We fix these three functions by comparing with the results of the simplest correlators derived from an explicit supergravity calculation.
We present a formula for the holographic 4-point correlators in AdS 3 × S 3 involving four singletrace operators of dimension k, k, l, l. As an input we use the supergravity results for the Heavy-Heavy-Light-Light correlators that can be derived by studying the linear fluctuations around known asymptotically AdS 3 × S 3 geometries. When the operators of dimension k and l are in the same multiplet there are contributions due to the exchange of single-trace operators in the t and u-channels, which are not captured by the approach mentioned above. However by rewriting the s-channel results in Mellin space we obtain a compact expression for the s-channel contribution that makes it possible to conjecture a formula for the complete result. We discuss some consistency checks that our proposal meets.
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