Ground states of supersymmetric matrix models. (English) Zbl 1055.81603

Graf, G. M.

Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1998-1999, Exp. No. XIII, 10 p. (1999).

Summary: We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the \(d= 9\) model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in \(d= 9\). Moreover, it would be unique. Other values of \(d\), where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation. This seminar is based on joint work with J. Fröhlich, G. M. Graf, D. Hasler, J. Hoppe and S.-T. Yau [Asymptotic form of zero energy wave functions in supersymmetric matrix models, Nucl. Phys. B 567, No. 1–2, 231–248 (2000; Zbl 0951.81083)].

MSC:

81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60	Supersymmetric field theories in quantum mechanics
83E30	String and superstring theories in gravitational theory
83E15	Kaluza-Klein and other higher-dimensional theories

Citations:

Zbl 0951.81083