Derivation of the Type IIB topological-term coupling

Derive the coupling of the additional topological term in the type IIB supergravity action from a worldsheet calculation, thereby determining the boundary polarization and holographic ensemble directly from the underlying string theory.

Background

The paper introduces an additional topological term in the PST formulation of type IIB supergravity to obtain a consistent variational principle for the self-dual five-form. The sign of this term selects either the fixed-flux or fixed-potential boundary polarization, corresponding respectively to the canonical or grand canonical boundary ensemble.

Although both signs produce consistent semiclassical bulk descriptions and reproduce the perturbative Schur-index partition functions, the underlying string-theoretic derivation of the coupling is not provided. Such a derivation would establish which boundary polarization is selected directly by quantized type IIB strings rather than by effective-supergravity consistency and holographic matching.

References

Contrary to M-theory, where there is a natural choice of ensemble since the supergravity action is written naturally in terms of the three-form gauge potential, in the IIB theory there is no preferred ensemble and instead the boundary polarisations are determined by the sign of the additional topological term in the IIB supergravity action, which remains to be derived from a worldsheet calculation.

— Holographic Ensembles in Type IIB  (2608.27956 - Muiden, 28 Aug 2026) in Section 1, Introduction, p. 4

For boundaries of more complicated topology the measure and contour of the ensemble changing integral are an open question, analysed for AdS4 in [8], and would be interesting to understand in more detail.

— Holographic Ensembles in Type IIB  (2608.27956 - Muiden, 28 Aug 2026) in Section 2.1, after Eq. (2.52), p. 10

It is still to be established if D3-brane giants turn out to be much simpler, at the quantum level, at fixed cel 4, compared to the fixed flux ensemble.

— Holographic Ensembles in Type IIB  (2608.27956 - Muiden, 28 Aug 2026) in Section 3, after Eq. (3.18), p. 12