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Title: Grassmann matrix quantum mechanics

We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic Hermitian matrix quantum mechanics. We describe the classical curved phase space that emerges in the low energy sector. The phase space lives on a compact Kähler manifold parameterized by a complex matrix, of the type discovered some time ago by Berezin. The emergence of a semiclassical bosonic matrix quantum mechanics at low energies requires that the original Grassmann matrices be in the long rectangular limit. In conclusion, we discuss possible holographic interpretations of such matrix models which, by construction, are endowed with a finite dimensional Hilbert space.
 [1] ;  [2] ;  [2]
  1. Institute for Advanced Study, Princeton, NJ (United States)
  2. Columbia Univ., New York, NY (United States); Instituut voor Theoretische Fysica, Leuven (Belgium)
Publication Date:
OSTI Identifier:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 4; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
Columbia Univ., New York, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS 1/N expansion; Matrix Models; Gauge-gravity correspondence