Superalgebra for M theory on a pp wave

Nakwoo Kim; Jeong-Hyuck Park

doi:10.1103/PhysRevD.66.106007

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Superalgebra for M theory on a pp wave

Nakwoo Kim^*

Jeong-Hyuck Park^†

Max-Planck-Institute für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany

School of Physics, Korea Institute for Advanced Study, 207-43, Cheongryangri-Dong, Dongdaemun-Gu, Seoul 130-012, Korea

^*Email address: kim@aei-potsdam.mpg.de
^†Email address: jhp@kias.re.kr

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Phys. Rev. D 66, 106007 – Published 26 November, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.106007

Abstract

We study the superalgebra of the M theory on a fully supersymmetric pp wave. We identify the algebra as the special unitary Lie superalgebra, $su (2 | 4; 2, 0)$ or $su (2 | 4; 2, 4),$ and analyze its root structure. We discuss the typical and atypical representations deriving the typicality condition explicitly in terms of the energy and other four quantum numbers. We classify the BPS multiplets preserving 4, 8, 12, 16 real supercharges and obtain the corresponding spectrum. We show that in the BPS multiplet either the lowest energy floor is an $su (2)$ singlet or the highest energy floor is an $su (4)$ singlet.

References (24)

D. Berenstein, J.M. Maldacena, and H. Nastase, J. High Energy Phys. 04, 013 (2002).
T. Banks, W. Fischler, S.H. Shenker, and L. Susskind, Phys. Rev. D 55, 5112 (1997).
B. de Wit, J. Hoppe, and H. Nicolai, Nucl. Phys. B305, 545 (1988).
J. Kowalski-Glikman, Phys. Lett. 134B, 194 (1984).
J. Figueroa-O’Farrill and G. Papadopoulos, J. High Energy Phys. 08, 036 (2001); M. Blau, J. Figueroa-O’Farrill, C. Hull, and G. Papadopoulos, Class. Quantum Grav. 19, L87 (2002).
K. Dasgupta, M.M. Sheikh-Jabbari, and M. Van Raamsdonk, J. High Energy Phys. 05, 056 (2002).
N. Kim and J. Plefka, “On the spectrum of pp-wave matrix theory,” hep-th/0207034.
V.G. Kac, Adv. Math. 26, 8 (1977).
V.G. Kac, Commun. Math. Phys. 53, 31 (1977).
R. Penrose, in Differential Geometry and Relativity, edited by Cahen Flato (Reidel, Dordrecht, Holland, 1976), pp. 271–275.
E. Inönü and E.P. Wigner, Proc. Natl. Acad. Sci. U.S.A. 39, 510 (1953); E. Inönü, in Group Theoretical Concepts and Methods in Elementary Particle Physics, edited by F. Gürsey (Gordon and Breach, New York, 1964).
M. Hatsuda, K. Kamimura, and M. Sakaguchi, Nucl. Phys. B637, 168 (2002).
M. Hatsuda, K. Kamimura, and M. Sakaguchi, Nucl. Phys. B632, 114 (2002).
J.-H. Park, Nucl. Phys. B539, 599 (1999).
S. Hyun and H. Shin, Phys. Lett. B 543, 115 (2002).
J.-H. Park, Nucl. Phys. B559, 455 (1999); J. Math. Phys. 41, 7129 (2000).
J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, 3rd revised ed. (Springer, New York, 1980).
W. Fulton, Young Tableaux (Cambridge University Press, Cambridge, UK, 1997).
J.P. Hurni and B. Morel, J. Math. Phys. 24, 157 (1983); ibid.24, 2250(E) (1983).
S. Ferrara and E. Sokatchev, J. Math. Phys. 42, 3015 (2001).
K. Dasgupta, M. Sheikh-Jabbari, and M. Van Raamsdonk, J. High Energy Phys. 09, 021 (2002).
D. Bak, K. Lee, and J.-H. Park, Phys. Rev. D 66, 025021 (2002).
D. Bak, “Supersymmetric branes in PP wave background,” hep-th/0204033.
K. Sugiyama and K. Yoshida, “BPS conditions of supermembrane on the pp-wave,” hep-th/0206132.

[c1] D. Berenstein, J.M. Maldacena, and H. Nastase, J. High Energy Phys. 04, 013 (2002).

[c2] T. Banks, W. Fischler, S.H. Shenker, and L. Susskind, Phys. Rev. D 55, 5112 (1997).

[c3] B. de Wit, J. Hoppe, and H. Nicolai, Nucl. Phys. B305, 545 (1988).

[c4] J. Kowalski-Glikman, Phys. Lett. 134B, 194 (1984).

[c5] J. Figueroa-O’Farrill and G. Papadopoulos, J. High Energy Phys. 08, 036 (2001); M. Blau, J. Figueroa-O’Farrill, C. Hull, and G. Papadopoulos, Class. Quantum Grav. 19, L87 (2002).

[c6] K. Dasgupta, M.M. Sheikh-Jabbari, and M. Van Raamsdonk, J. High Energy Phys. 05, 056 (2002).

[c7] N. Kim and J. Plefka, “On the spectrum of pp-wave matrix theory,” hep-th/0207034.

[c8] V.G. Kac, Adv. Math. 26, 8 (1977).

[c9] V.G. Kac, Commun. Math. Phys. 53, 31 (1977).

[c10] R. Penrose, in Differential Geometry and Relativity, edited by Cahen Flato (Reidel, Dordrecht, Holland, 1976), pp. 271–275.

[c11] E. Inönü and E.P. Wigner, Proc. Natl. Acad. Sci. U.S.A. 39, 510 (1953); E. Inönü, in Group Theoretical Concepts and Methods in Elementary Particle Physics, edited by F. Gürsey (Gordon and Breach, New York, 1964).

[c12] M. Hatsuda, K. Kamimura, and M. Sakaguchi, Nucl. Phys. B637, 168 (2002).

[c13] M. Hatsuda, K. Kamimura, and M. Sakaguchi, Nucl. Phys. B632, 114 (2002).

[c14] J.-H. Park, Nucl. Phys. B539, 599 (1999).

[c15] S. Hyun and H. Shin, Phys. Lett. B 543, 115 (2002).

[c16] J.-H. Park, Nucl. Phys. B559, 455 (1999); J. Math. Phys. 41, 7129 (2000).

[c17] J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, 3rd revised ed. (Springer, New York, 1980).

[c18] W. Fulton, Young Tableaux (Cambridge University Press, Cambridge, UK, 1997).

[c19] J.P. Hurni and B. Morel, J. Math. Phys. 24, 157 (1983); ibid.24, 2250(E) (1983).

[c20] S. Ferrara and E. Sokatchev, J. Math. Phys. 42, 3015 (2001).

[c21] K. Dasgupta, M. Sheikh-Jabbari, and M. Van Raamsdonk, J. High Energy Phys. 09, 021 (2002).

[c22] D. Bak, K. Lee, and J.-H. Park, Phys. Rev. D 66, 025021 (2002).

[c23] D. Bak, “Supersymmetric branes in PP wave background,” hep-th/0204033.

[c24] K. Sugiyama and K. Yoshida, “BPS conditions of supermembrane on the pp-wave,” hep-th/0206132.

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Superalgebra for M theory on a pp wave

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