A double-scaling large-d saddle for mass-deformed BFSS/BMN matrix QM interpolates between commutator-dominated and mass-dominated regimes, yielding BFSS_{2}-like low-T uniform-holonomy dynamics and IKKT-like high-T almost-commuting behavior.
Phases of one dimensional large N gauge theory in a 1/D expansion
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abstract
We consider large N Yang Mills theory with D adjoint scalar fields in d dimensions for d=0 or 1. We show the existence of a non-trivial saddle point of the functional integral at large D which is characterized by a mass gap for the adjoint scalars. We integrate out the adjoint scalars in a 1/D expansion around the saddle point. In case of one dimension which is regarded as a circle, this procedure leads to an effective action for the Wilson line. We find an analogue of the confinement/deconfinement transition which consists of a second order phase transition from a uniform to a non-uniform eigenvalue distribution of the Wilson line, closely followed by a Gross-Witten-Wadia transition where a gap develops in the eigenvalue distribution. The phase transition can be regarded as a continuation of a Gregory-Laflamme transition. Our methods involve large values of the dimensionless 'tHooft coupling. The analysis in this paper is quantitatively supported by earlier numerical work for D=9.
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hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Establishes equivalence between endpoint and Molien-Weyl formulations for large-d BFSS models on the lattice and derives finite continuum D-channel via a toy holonomy potential model.
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A Double--Scaling Large--\(d\) Saddle of BFSS/BMN Matrix Quantum Mechanics
A double-scaling large-d saddle for mass-deformed BFSS/BMN matrix QM interpolates between commutator-dominated and mass-dominated regimes, yielding BFSS_{2}-like low-T uniform-holonomy dynamics and IKKT-like high-T almost-commuting behavior.
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Endpoint formulation and Molien--Weyl structure for the \(N=2\), large--\(d\) BFSS/BMN models
Establishes equivalence between endpoint and Molien-Weyl formulations for large-d BFSS models on the lattice and derives finite continuum D-channel via a toy holonomy potential model.