On Toda Equation and Half BPS Supergravity Solution in M-Theory

Details On Toda Equation and Half BPS Supergravity Solution in M-Theory On Toda Equation and Half BPS Supergravity Solution in M-Theory

2005-11-14

arxiv.org/abs/hep-th/0511145v2

JHEP0601:026,2006

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, no figures

Scientific paper

10.1088/1126-6708/2006/01/026

Recently, it was shown that half BPS Supergravity solution of theories with SU(2$|$4) symmetry algebra is given uniformly by determining a single function which obeys three dimensional continuous Toda equation. In this paper, we study the scale invariant solution of Toda equation. Our motivation is that some solutions of half BPS sector of IIB supergravity, as one excepts from the fermion description of the theory, are scale invariant. By defining two auxiliary functions we prove that such solutions of Toda equation obey cubic algebraic equation. We obtain some simpl solutions of Toda equation specially, we observe that the PP-wave solution can be written in this fashion.

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