Proof of the absence of further inverse-chemical-potential corrections

Prove directly in the twisted AdS5 × S5 type IIB bulk that the perturbative partition function has no corrections beyond the classical quadratic term and the one-loop Kaluza–Klein determinant, in particular that all further 1/μ corrections vanish.

Background

The bulk computation determines the classical contribution proportional to μ² and the massive-mode one-loop contribution through the Kaluza–Klein determinant. The authors argue, based on comparison with the boundary grand canonical Schur partition function, that no additional inverse powers of μ occur.

A direct bulk proof is not supplied. The paper identifies supersymmetric localization of type IIB theory as the apparent method needed to establish the vanishing of these corrections from first principles.

References

We have not derived that there are no further 1/μ corrections, but we will see upon comparison to the boundary partition function that those must in fact vanish. Proving this statement directly in the bulk would seem to require a direct supersymmetric localization procedure of the IIB theory.

— Holographic Ensembles in Type IIB  (2608.27956 - Muiden, 28 Aug 2026) in Section 2.1, Supersymmetric thermal AdS, around Eq. (2.46), p. 9

Whether analogous simplifications exist in the IIB setup remains to be studied.

— Holographic Ensembles in Type IIB  (2608.27956 - Muiden, 28 Aug 2026) in Section 4, Future directions, p. 14