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Integrable systems from supergravity BPS equations · Around

2008

Integrable systems from supergravity BPS equations

D'Hoker, Eric, Estes, John

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Integrable systems of the sine-Gordon/Liouville type, which arise from reducing the BPS equations for solutions invariant under 16 supersymmetries in Type IIB supergravity and M-theory, are shown to be special cases of an infinite family of integrable systems, parametrized by an arbitrary real function $f$ of a real variable.

It is shown that, for each function $f$, this generalized integrable system may be mapped onto a system of linear equations, which in turn may be integrated in terms of the two linearly independent solutions of an ordinary linear second order differential equation which depends only on the function $f$.

Built on

L.D. Faddeev, and L.A. Takhtajan,
1980
Earlier work this paper cites.
Mark J. Ablowitz and Harvey Segur,
1981
Earlier work this paper cites.
E. D’Hoker and R. Jackiw, “Liouville Field Theory,” Phys. Rev. D
1982
Earlier work this paper cites.
E. D’Hoker and R. Jackiw, “Space Translation Breaking And Compactification In The Liouville Theory,” Phys. Rev. Lett
1983
Earlier work this paper cites.

Similar

E. D’Hoker, D. Z. Freedman and R. Jackiw, “SO(2,1) Invariant Quantization Of The Liouville Theory,” Phys. Rev. D
1983
Cited alongside, same era.
J. P. Gauntlett and S. Pakis, “The geometry of D = 11 Killing spinors. ((T),” JHEP
2003
Cited alongside, same era.
J. P. Gauntlett, D. Martelli, S. Pakis and D. Waldram, Commun. Math. Phys
2004
Cited alongside, same era.
J. P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Class. Quant. Grav
2004
Cited alongside, same era.
E. D’Hoker, J. Estes, M. Gutperle and D. Krym, “Exact Half-BPS Flux Solutions in M-theory I, Local Solutions,” arXiv:0806.0605 [hep-th]
Original
Cited in the paper.

Then

H. Lin, O. Lunin and J. M. Maldacena, “Bubbling AdS space and 1/2 BPS geometries,” JHEP
2004
Later among the works it cites.
E. D’Hoker, J. Estes and M. Gutperle, “Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus,” JHEP
Original
2007
Later among the works it cites.
E. D’Hoker, J. Estes and M. Gutperle, “Gravity duals of half-BPS Wilson loops,” JHEP
Original
2007
Later among the works it cites.

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