Center for diffusion of mathematic journals
Seminar Homepage
Séminaire Équations aux dérivées partielles (Polytechnique)
Table of contents for this volume | Previous article | Next articleGian Michele Graf
Ground states of supersymmetric matrix models
Séminaire Équations aux dérivées partielles (Polytechnique) (1998-1999), Exp. No. 13, 8 p.
Article PDF | Reviews MR 1721331 | Zbl 1055.81603
Résumé - Abstract
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, D. Hasler, J. Hoppe and S.-T. Yau.
Bibliography
[2] T. Banks, W. Fischler, S.H. Shenker, L. Susskind, M theory as a matrix model : a conjecture, Phys. Rev. D55, 5112-5128 (1997) ; hep-th/9610043. MR 1449617
[3] M. Claudson, M. Halpern, Supersymmetric ground state wave functions, Nucl. Phys. B250, 689-715 (1985). MR 780110
[4] E.A. Coddington, N. Levinson, Theory of ordinary differential equations, Krieger (1987).
[5] J. Fröhlich, J. Hoppe, On zero–mass ground states in super–membrane matrix models. Comm. Math. Phys. 191, 613-626 (1998) ; hep-th/9701119. MR 1608539 | Zbl 0911.46046
[6] J. Fröhlich, G.M. Graf, D. Hasler, J. Hoppe, S.-T. Yau, Asymptotic form of zero energy wave functions in supersymmetric matrix models, hep-th/9904182. arXiv
[7] J. Goldstone, unpublished. J. Hoppe, Quantum theory of a massless relativistic surface, MIT Ph.D. Thesis (1982) ; Proceedings of the workshop Constraints theory and relativistic dynamics, World Scientific (1987).
[8] M.B. Halpern, C. Schwartz, Asymptotic search for ground states of SU(2) matrix theory, Int. J. Mod. Phys. A13, 4367-4408 (1998) ; hep-th/9712133. MR 1647027 | Zbl 0937.81057
[9] A. Konechny, On asymptotic Hamiltonian for SU(N) matrix theory, JHEP 9810 (1998) ; hep-th/9805046. MR 1660433
[10] S. Sethi, M. Stern, D–Brane bound state redux. Comm. Math. Phys. 194, 675-705 (1998) ; hep-th/9705046. arXiv | MR 1631497 | Zbl 0911.53052
[11] B. Simon, Some quantum operators with discrete spectrum but classically continuous spectrum, Ann. Phys. 146, 209-220 (1983). MR 701264 | Zbl 0547.35039
[12] B. Simon, Representations of finite and compact groups, American Mathematical Society (1996). MR 1363490 | Zbl 0840.22001
[13] B. de Wit, J. Hoppe, H. Nicolai, On the quantum mechanics of supermembranes, Nucl. Phys. B305, 545-581 (1988). MR 984284
[14] B. de Wit, M. Lüscher, H. Nicolai, The supermembrane is unstable, Nucl. Phys. B320, 135-159 (1989). MR 1003285
[15] E. Witten, Bound states of strings and $p$–branes. Nuclear Phys. B460, 335-350 (1996) ; hep-th/9510135. MR 1377168 | Zbl 1003.81527
[16] P. Yi, Witten index and threshold bound states of D-branes, Nucl. Phys. B505, 307-318 (1997) ; hep-th/9704098. MR 1483841 | Zbl 0925.58105