A supergravity dual for IKKT holography

TL;DR

This paper constructs a supergravity dual for the IKKT matrix model, establishing a holographic dictionary and analyzing supersymmetric solutions within a one-dimensional gauged supergravity framework.

Contribution

It explicitly constructs a one-dimensional maximal gauged supergravity encoding the dynamics of the IKKT model's holographic dual and explores its supersymmetric solutions.

Findings

Established the holographic dictionary for the IKKT matrix model.

Constructed the full non-linear supergravity Lagrangian up to second order in fermions.

Derived classes of half-supersymmetric solutions and their uplifts.

Abstract

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.