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

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

Zbl 0951.81083
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