Supersymmetry protection (non-renormalization) of a specific non-extremal family of four-point correlators

Determine whether the non-extremal four-point functions of chiral primaries in AdS3×S3×T4 that satisfy the sphere condition and match symmetric orbifold predictions (including spectrally flowed sectors) are protected by supersymmetry. Concretely, establish a non-renormalization theorem proving that correlators of the form ⟨O_n^+(0) O_2^−(1) O_{n+2}^{−†}(∞) O_2^{−†}(x,x)⟩ (and their flowed analogues) are supersymmetry-protected across the moduli space, by working within the boundary SCFT.

Background

The authors extend prior observations for unflowed correlators to spectrally flowed sectors, finding precise agreement between worldsheet computations and symmetric orbifold predictions for a non-extremal family of four-point functions that nonetheless meets the sphere genus-zero condition.

They argue that this persistent agreement suggests these correlators may be protected by supersymmetry, i.e., subject to a non-renormalization theorem, but note that such protection has not yet been firmly established. A definitive proof would clarify the status of these observables and broaden the class of protected quantities in the AdS3/CFT2 correspondence.

Proving protection for this family would also illuminate how non-protected processes behave away from the tensionless point and inform the structure of marginal deformations in the dual SCFT.