A Double--Scaling Large--\(d\) Saddle of BFSS/BMN Matrix Quantum Mechanics

High Energy Physics - Theory [Submitted on 16 Jun 2026] Title:A Double--Scaling Large--\(d\) Saddle of BFSS/BMN Matrix Quantum Mechanics View PDF HTML (experimental)Abstract:We study the large--\(d\) dynamics of the mass--deformed bosonic \(\mathrm{BFSS}_{d+1}\) matrix quantum mechanics using a Hubbard--Stratonovich localization of the Yang--Mills interaction. After integrating out the matrix coordinates, the theory reduces to a holonomy--dependent effective action for an auxiliary adjoint kernel. We introduce a commuting--symmetric saddle and its maximally symmetric specialization, in which the interaction is encoded in a single dynamically generated mass shift \(k_0\). The resulting large--\(d\) description is a gauged matrix harmonic oscillator with self--consistent frequency \(s^2=m+k_0\), fixed by a gap equation. We analyze the low--temperature \(X\)-space physics, the holonomy effective action, the Yang--Mills observable, and the associated phase structure. We then identify a correlated double--scaling limit in which \(d\to\infty\), \(m\to\infty\), and \(\kappa=m^{3/2}/d\) is held fixed. In this limit the Yang--Mills interaction and the explicit mass deformation remain parametrically balanced: the theory interpolates between the commutator--dominated BFSS regime and the mass--dominated Gaussian regime. The double--scaled theory exhibits two complementary large--\(d\) regimes. At low temperature, the enhanced gap pushes the deconfinement scale upward and opens a parametrically large uniform--holonomy region, where the bulk dynamics behaves as weakly coupled \(\mathrm{BFSS}_2\)--type gauged harmonic--oscillator sectors. At the same time, the high--temperature branch reveals an overlap window in which the Gaussian description remains self--consistent while the commutator contribution per matrix pair is parametrically suppressed. The resulting dynamics is therefore \(\mathrm{BFSS}_2\)--like in its enlarged uniform--holonomy sector and IKKT--like in its almost--commuting matrix behavior. Current browse context: hep-th References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.