The Polarised IKKT Matrix Model

Sean A. Hartnoll; Jun Liu

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arXiv · 2409.18706

The Polarised IKKT Matrix Model

Sean A. Hartnoll·Jun Liu

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Abstract

We establish a correspondence between a supersymmetric mass deformation of the IKKT matrix integral at large $N$ and a background of Euclidean type IIB string theory. Both sides have sixteen supersymmetries and an $SO(3)\times SO(7)$ symmetry. In the limit of large mass the integral is dominated by a fuzzy sphere saddle point. This saddle corresponds to a Euclidean $D1$-brane in a finite, Euclidean, ellipsoidal cavity. The cavity is supported by three-form NSNS flux that polarises $N$ $D$-instantons into the $D1$-brane. We furthermore use supersymmetric localisation to show that the deformed matrix integral can be reduced to a moduli space integral, allowing exact results away from the large mass limit. At small mass the $D1$-branes can backreact on the geometry, and we discuss the possible formulation of a `timeless' holography in such regimes.

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Sean A. Hartnoll, Jun Liu. 2024-09-27. The Polarised IKKT Matrix Model. https://arxiv.org/abs/2409.18706

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