The CFT$$_6$$ origin of all tree-level 4-point correlators in AdS$$_3 \times S^3$$

Abstract

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.

More on holographic correlators: twisted and dimensionally reduced structures

“…The generating function is nothing but the stress tensor four-point function after replacing four dimensional distances with ten dimensional distances. A similar six dimensional version was also discovered for AdS 3 × S 3 × K3 correlators [17,18]. However, it is generally believed that the hidden conformal symmetry is non-existent for backgrounds which are not conformally flat (such as AdS 4 ×S 7 and AdS 7 × S 4 ).…”

“…The relevant superconformal algebra in this case is psu(2, 2|4) which, as discussed in [20], admits a chiral algebra subsector whose currents come from Schur multiplets of the 4d theory. 18 Furthermore, when N > 2 in d = 4, the chiral algebra contains supercurrents of its own. This leads to a global subalgebra of psu(1, 1|2) when N = 4.…”

“…We will denote these currents as J (k) a 1 ...a 2j and contract them with polarization vectors as in (2.16). Their sl(2) and su(2) spins (which must be equal) are given 18 Again, the twisted translation (4.1) must be applied to the Schur operators. This time, the maximal subalgebra is su(2) × su(2) × u(1) ⊂ su(4) which means that an su(2) R-symmetry survives in the chiral algebra.…”

The Regge limit of AdS3 holographic correlators

“…In fact, generic conical defect geometries are not dual to pure states and it would be interesting to understand whether the CFT data extracted from them are fully consistent solutions of the bootstrap relation. As an aside, let us highlight that setting N b = 1 in the HHLL correlators described above, as done in [40][41][42], reproduces the correlators of all light states in AdS 3 ×S 3 [41,43], despite the two regimes being not obviously connected. We analyse the Regge conformal bootstrap also in this regime, providing an explicit AdS 3 /CFT 2 example of the analysis in [11,12] and showing that the information obtained in the Regge regime can be used to fix some CFT data for spin-2 operators that was left undetermined in [40].…”

All Tree-Level Correlators for M Theory on AdS7×S4

“…This is perhaps an indication that a slightly different definition of the reduced amplitude is needed. It would be interesting to study this in detail and see if hidden structures emerge, which is akin to what happens in related contexts [30][31][32][33]. On a more practical level, (25) contains a wealth of CFT data.…”