A supergravity dual for IKKT holography

The IKKT matrix model, from the holographic perspective, arises at the p=-1 endpoint of the family of dualities relating type II supergravities on near-horizon Dp-brane geometries to (p+1)-dimensional super Yang-Mills theories with sixteen supercharges. In this work, we detail and expand results reported in a recent letter by establishing the holographic dictionary between gauge-invariant operators in the lowest BPS multiplet of the matrix model and the corresponding Kaluza-Klein fluctuations of Euclidean IIB supergravity compactified on the D(-1) instanton background. The full non-linear dynamics of these fluctuations can be encoded in a one-dimensional maximal gauged supergravity, which we construct explicitly. We provide its complete Lagrangian, up to second order in fermions, together with the corresponding supersymmetry transformations. We further discuss real forms of the theory for non-compact gauge groups and their embeddings into ten-dimensional supergravities with Lorentzian signature. From the analysis of the one-dimensional Killing spinor equations, we derive different classes of half-supersymmetric solutions, and discuss their uplifts as well as their relations to known solutions.

💡 Research Summary

The paper establishes a concrete holographic correspondence between the zero‑dimensional IKKT matrix model and type IIB supergravity on the D(‑1) instanton background, which sits at the p = −1 endpoint of the familiar Dp‑brane family of gauge/gravity dualities. The authors first analyse the gauge‑invariant single‑trace operators of the IKKT model. Using the SO(10) representation content of the bosonic matrices X^a and fermionic matrices Ψ^α, together with the field‑equation constraints, they construct a single‑letter partition function Z₁(t) that encodes the scaling weights. Applying Polya’s enumeration theorem they obtain the full cyclic word generating function Z_IKKT(t), which reproduces the spectrum of operators organised into infinite towers of long and short supermultiplets. The shortest short multiplet B₁ coincides with the single‑letter partition function, while the generic BPS multiplet B_n contains a traceless symmetric SO(10) tensor of rank n together with 128 × dim R fermionic states, where dim R is the dimension of the