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<p>We establish a correspondence between a supersymmetric mass deformation of the IKKT matrix integral at large <i>N</i> and a background of Euclidean type IIB string theory. Both sides have sixteen supersymmetries and an SO(3) × 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 <i>D</i>1-brane in a finite, Euclidean, ellipsoidal cavity. The cavity is supported by three-form NSNS flux that polarises <i>N D</i>-instantons into the <i>D</i>1-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 <i>D</i>1-branes can backreact on the geometry, and we discuss the possible formulation of a ‘timeless’ holography in such regimes.</p>

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The polarised IKKT matrix model

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  • 发表日期：

    2025年3月7日

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  • Sean A. Hartnoll,
  • Jun Liu

摘要

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) × 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.