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Spin(9) average of SU(N) matrix models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-3456-5846
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2009 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 4, 043510-1-043510-7 p.Article in journal (Refereed) Published
Abstract [en]

We apply a method of group averaging to states and operators appearing in (truncations of) the Spin(9)xSU(N) invariant matrix models. We find that there is an exact correspondence between the standard supersymmetric Hamiltonian and the Spin (9) average of a relatively simple lower-dimensional model.

Place, publisher, year, edition, pages
American Institute of Physics , 2009. Vol. 50, no 4, 043510-1-043510-7 p.
Keyword [en]
supersymmetric matrix models, zero-energy states, group averaging, harmonic oscillator, matrix-Schrödinger operator
National Category
Other Physics Topics Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-12841DOI: 10.1063/1.3105925ISI: 000266596800036Scopus ID: 2-s2.0-65549137712OAI: oai:DiVA.org:kth-12841DiVA: diva2:319247
Note
QC20100629Available from: 2010-05-17 Created: 2010-05-17 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Zero-energy states in supersymmetric matrix models
Open this publication in new window or tab >>Zero-energy states in supersymmetric matrix models
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The work of this Ph.D. thesis in mathematics concerns the problem of determining existence, uniqueness, and structure of zero-energy states in supersymmetric matrix models, which arise from a quantum mechanical description of the physics of relativistic membranes, reduced Yang-Mills gauge theory, and of nonperturbative features of string theory, respectively M-theory. Several new approaches to this problem are introduced and considered in the course of seven scientific papers, including: construction by recursive methods (Papers A and D), deformations and alternative models (Papers B and C), averaging with respect to symmetries (Paper E), and weighted supersymmetry and index theory (Papers F and G). The mathematical tools used and developed for these approaches include Clifford algebras and associated representation theory, structure of supersymmetric quantum mechanics, as well as spectral theory of (matrix-) Schrödinger operators.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. 88 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 10:06
Keyword
supermembrane matrix models, supersymmetric quantum mechanics, zero-energy states, Clifford algebra, matrix-valued Schrödinger operator, spectral theory, bounds for negative eigenvalues
National Category
Mathematics Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-12846 (URN)978-91-7415-662-1 (ISBN)
Public defence
2010-06-04, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 14:00 (English)
Opponent
Supervisors
Note
QC20100629Available from: 2010-05-19 Created: 2010-05-17 Last updated: 2010-06-29Bibliographically approved

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Lundholm, Douglas

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