Holography for the IKKT matrix model

概要

A particularly interesting corner of holographic dualities is the correspondence between type II strings on near-horizon Dp branes geometries and d = p+1 dimensional super Yang-Mills theories with sixteen supercharges. For the extremal case p=-1, this suggests a holographic duality for the IKKT matrix model. Despite intriguing and highly non-trivial results in the IKKT model, this duality has so far remained largely unexplored. In this talk, I will consider the lowest supermultiplet of gauge invariant operators of the model and identify its states with the lowest Kaluza-Klein fluctuations of (Euclidean) IIB supergravity on the D(-1) instanton background. I will explain how to construct its holographic bulk realisation as a one-dimensional maximal supergravity with 32 supercharges and local SO(10) invariance, capturing the full non-linear dynamics. By analysing the bulk Killing spinor equations, I will present a general class of half-supersymmetric solutions that typically break SO(10), and discuss their uplifts to IIB supergravity. I will end with some remarks on open questions and future directions.

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