A preprint reports that the key distinction between two boundary ensembles in a type IIB holographic calculation is a sign in the bulk action. The analysis assigns plus one to fixed magnetic flux, the fixed-rank or canonical description on the boundary, and minus one to fixed electric potential, the fixed-chemical-potential or grand-canonical description. In plain terms, the sign selects which member of a conjugate pair is held fixed at the boundary.
The work is a theoretical calculation with no empirical population or data. It studies a Schur-twisted type IIB setup on AdS5 × S5, with supersymmetric thermal boundary conditions and twists on the thermal circle. Its question is whether the bulk partition function can reproduce the boundary Schur-index partition function in fixed-flux or fixed-rank and fixed-potential or grand-canonical forms.
A boundary choice built into the action
The added topological term is treated as a total derivative. In the paper’s calculation, that leaves the bulk equations of motion unchanged but alters boundary terms and the on-shell action, the value of the action on the solution. The result is interpreted as two consistent boundary polarizations of the same IIB theory.
The connection is expressed through Hamilton-Jacobi relations. In the fixed-potential ensemble, changing the chemical potential changes the action according to minus the flux number. In the fixed-flux ensemble, changing the flux number changes the action according to plus the chemical potential. The authors describe this as a Legendre transform linking the two ways of holding a boundary quantity fixed.
At the Schur point, in the supersymmetric renormalization scheme used by the paper, the fixed-potential action is a negative quadratic in the chemical potential divided by the thermal-circle parameter. After the Legendre transform, the fixed-flux action is the thermal-circle parameter times the square of the flux number divided by four in the stated limit where the AdS radius is large compared with the string length. The chemical potential is conjugate to the quantized flux number, which is dual to the boundary rank.
The perturbative match is the central result
The bulk’s one-loop contribution is a Kaluza-Klein determinant for massive modes. The paper obtains it from the single-particle supergravity index and its plethystic exponential, including local fields and the singleton, instead of evaluating the determinant directly. In the Schur limit, that procedure supplies the factor used in the partition function.
On the boundary, supersymmetric localization provides a matrix-model representation of the fixed-rank partition function on S1 × S3. To construct the grand-canonical bulk expression, the calculation sums over all copies related by large-gauge transformations so that the result remains invariant. Its overall normalization is attributed to the string measure and fixed by trivializing the conjugate partition function in the zero-flux sector.
That machinery leads to the paper’s central check: exact agreement between perturbative bulk and boundary expressions in both ensembles. The grand-canonical boundary grand potential equals the perturbative bulk contribution. At fixed rank, the coefficient consists of the one-loop Kaluza-Klein factor multiplied by an exponential whose exponent is minus the thermal-circle parameter times the squared rank divided by four, and it equals the corresponding bulk coefficient. The agreement concerns the perturbative terms in this case study.
The exact corrections split into two different stories
The exact grand-canonical result has a more economical form. The paper writes the exact grand potential as the perturbative answer evaluated at an effective chemical potential that includes nonperturbative renormalization. The nonperturbative part is the difference between the square of that effective potential and the square of the original potential, divided by the thermal-circle parameter, and the exact-to-perturbative difference is exponentially suppressed. The correction sector is therefore packaged as a renormalization of the chemical potential.
The same information becomes less tidy after returning to fixed flux. The paper associates the expansion with m giant gravitons and reports that, for wrapping number m, polynomial dependence on the flux number can reach order m. It presents this as a structural pattern rather than a complete fixed-flux brane derivation.
What remains unresolved
Several important derivations remain open. The coupling of the topological term and its boundary terms are not derived from direct worldsheet quantization. Nor is the overall normalization derived from first-principles string quantization, since it is fixed by the zero-flux condition. The absence of further inverse-chemical-potential corrections is inferred through comparison with the boundary result rather than derived directly in the bulk.
Questions about the measure and contour for changing ensembles on more complicated boundary topologies also remain open. The analysis is centered on the Schur index in one Schur-twisted AdS5 × S5 setup, so it does not establish the same matching for black holes, black strings, more complicated topologies, or other observables. The supplied document is an arXiv preprint, version 1, dated 28 August 2026.
Paper data and sources
Original title: Holographic Ensembles in Type IIB
Authors: Jesse van Muiden
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text