Ground states of supersymmetric matrix models
Graf, Gian Michele1
1 Theoretische Physik, ETH-Hönggerberg, CH–8093 Zürich
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 13, 8 p.

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.

Graf, Gian Michele 1

1 Theoretische Physik, ETH-Hönggerberg, CH–8093 Zürich 
@article{SEDP_1998-1999____A13_0,
     author = {Graf, Gian Michele},
     title = {Ground states of supersymmetric matrix models},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:13},
     pages = {1--8},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1998-1999},
     zbl = {1055.81603},
     mrnumber = {1721331},
     language = {fr},
     url = {http://archive.numdam.org/item/SEDP_1998-1999____A13_0/}
}
TY  - JOUR
AU  - Graf, Gian Michele
TI  - Ground states of supersymmetric matrix models
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:13
PY  - 1998-1999
SP  - 1
EP  - 8
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://archive.numdam.org/item/SEDP_1998-1999____A13_0/
LA  - fr
ID  - SEDP_1998-1999____A13_0
ER  - 
%0 Journal Article
%A Graf, Gian Michele
%T Ground states of supersymmetric matrix models
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:13
%D 1998-1999
%P 1-8
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%U http://archive.numdam.org/item/SEDP_1998-1999____A13_0/
%G fr
%F SEDP_1998-1999____A13_0
Graf, Gian Michele. Ground states of supersymmetric matrix models. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 13, 8 p. http://archive.numdam.org/item/SEDP_1998-1999____A13_0/

[1] M. Baake, P. Reinicke, V. Rittenberg, Fierz identities for real Clifford algebras and the number of supercharges, J. Math. Phys. 26, 1070-1071 (1985). | MR | Zbl

[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

[3] M. Claudson, M. Halpern, Supersymmetric ground state wave functions, Nucl. Phys. B250, 689-715 (1985). | MR

[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 | Zbl

[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.

[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 | Zbl

[9] A. Konechny, On asymptotic Hamiltonian for SU(N) matrix theory, JHEP 9810 (1998) ; hep-th/9805046. | MR

[10] S. Sethi, M. Stern, D–Brane bound state redux. Comm. Math. Phys. 194, 675-705 (1998) ; hep-th/9705046. | MR | Zbl

[11] B. Simon, Some quantum operators with discrete spectrum but classically continuous spectrum, Ann. Phys. 146, 209-220 (1983). | MR | Zbl

[12] B. Simon, Representations of finite and compact groups, American Mathematical Society (1996). | MR | Zbl

[13] B. de Wit, J. Hoppe, H. Nicolai, On the quantum mechanics of supermembranes, Nucl. Phys. B305, 545-581 (1988). | MR

[14] B. de Wit, M. Lüscher, H. Nicolai, The supermembrane is unstable, Nucl. Phys. B320, 135-159 (1989). | MR

[15] E. Witten, Bound states of strings and p–branes. Nuclear Phys. B460, 335-350 (1996) ; hep-th/9510135. | MR | Zbl

[16] P. Yi, Witten index and threshold bound states of D-branes, Nucl. Phys. B505, 307-318 (1997) ; hep-th/9704098. | MR | Zbl