Grassmann matrix quantum mechanics

Anninos, Dionysios; Denef, Frederik; Monten, Ruben

doi:10.1007/JHEP04(2016)138

Title: Grassmann matrix quantum mechanics

Journal Article · Thu Apr 21 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP04(2016)138· OSTI ID:1326967

Anninos, Dionysios ^[1]; Denef, Frederik ^[2]; Monten, Ruben ^[2]

Institute for Advanced Study, Princeton, NJ (United States)
Columbia Univ., New York, NY (United States); Instituut voor Theoretische Fysica, Leuven (Belgium)

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.

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Research Organization:: Columbia Univ., New York, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0011941

OSTI ID:: 1326967

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 4; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 13 works

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References (21)

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Cited By (2)

Infrared realization of dS 2 in AdS 2 Anninos, Dionysios; Hofman, Diego M. Classical and Quantum Gravity, Vol. 35, Issue 8 https://doi.org/10.1088/1361-6382/aab143	journal	March 2018
Infrared Realization of dS$_2$ in AdS$_2$ Anninos, Dionysios; Hofman, Diego M. arXiv https://doi.org/10.48550/arxiv.1703.04622	text	January 2017

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