Asymptotic form of zero energy wave functions in supersymmetric matrix models. (English) Zbl 0951.81083

Summary: We derive the power law decay, and asymptotic form, of SU\((2)\times \text{Spin}(d)\) invariant wavefunctions satisfying \(Q_{\beta}\psi=0\) for all \(s_d=2(d-1)\) supercharges of reduced \((d+1)\)-dimensional supersymmetric SU(2) Yang-Mills theory, or, respectively, the SU(2) matrix model related to supermembranes in \(d+2\) dimensions.


81T60 Supersymmetric field theories in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
Full Text: DOI arXiv


[1] J. Goldstone, unpublished.
[2] J. Hoppe, Quantum theory of a massless relativistic surface, MIT Ph.D. Thesis (1982).
[3] J. Hoppe, Proc. Workshop Constraints theory and relativistic dynamics (World Scientific, Singapore, 1987).
[4] Claudson, M.; Halpern, M., Nucl. phys. B, 250, 689, (1985)
[5] Flume, R., Ann. phys., 164, 189, (1985)
[6] Baake, M.; Reinicke, P.; Rittenberg, V., J. math. phys., 26, 1070, (1985)
[7] de Wit, B.; Hoppe, J.; Nicolai, H., Nucl. phys. B, 305, 545, (1988)
[8] de Wit, B.; Lüscher, M.; Nicolai, H., Nucl. phys. B, 320, 135, (1989)
[9] Banks, T.; Fischler, W.; Shenker, S.H.; Susskind, L., Phys. rev. D, 55, 5112, (1997)
[10] Witten, E., Nucl. phys. B, 460, 335, (1996)
[11] Fröhlich, J.; Hoppe, J., Comm. math. phys., 191, 613, (1998)
[12] J. Hoppe, S.-T. Yau, Absence of zero energy states in reduced SU(N) 3d supersymmetric Yang-Mills theory, hep-th/9711169.
[13] J. Hoppe, S.-T. Yau, Absence of zero energy states in the simplest d=3 (d=5?) matrix models, hep-th/9806152.
[14] Yi, P., Nucl. phys. B, 505, 307, (1997)
[15] Sethi, S.; Stern, M., Comm. math. phys., 194, 675, (1998)
[16] Porrati, M.; Rozenberg, A., Nucl. phys. B, 515, 184, (1998)
[17] J. Hoppe, On the construction of zero energy states in supersymmetric matrix models I, II, III, hep-th/9709132, hep-th/9709217, hep-th/9711033.
[18] M.B. Green, M. Gutperle, JHEP 9801 (1998), hep-th/9711107.
[19] Halpern, M.B.; Schwartz, C., Int. J. mod. phys. A, 13, 4367, (1998)
[20] Krauth, W.; Nicolai, H.; Staudacher, M., Phys. lett. B, 431, 31, (1998)
[21] A. Konechny, JHEP 9810 (1998), hep-th/9805046.
[22] A.V. Smilga, Super Yang-Mills quantum mechanics and supermembrane spectrum, Proc. 1989 Trieste Conference, ed. M. Duff, C. Pope, E. Sezgin (World Scientific, Singapore, 1990).
[23] G.M. Graf, J. Hoppe, Asymptotic ground state for 10-dimensional reduced supersymmetric SU(2) Yang-Mills theory, hep-th/9805080.
[24] E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations (Krieger, 1987). · Zbl 0064.33002
[25] R.S. Palais, C. Terng, Critical Point Theory and Submanifold Geometry (Springer, Berlin, 1988). · Zbl 0658.49001
[26] B. Simon, Representations of Finite and Compact Groups (American Mathematical Society, Providence, 1996). · Zbl 0840.22001
[27] W.G. McKay, J. Patera, Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras (Marcel Dekker, New York, 1981). · Zbl 0448.17001
[28] I. Avramidi, On strict positivity of some matrix-valued differential operators, work in progress.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.