On Toda equation and half BPS supergravity solution in M-theory

2005/11/30 by Mohammad A. Ganjali · 3 citations
Mathematics · Physics and Astronomy · #Algebraic number #Black Holes and Theoretical Physics #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Scale invariance #Supergravity #Supersymmetry #Symmetry (geometry) #hep-th

paper · pdf · doi:10.1088/1126-6708/2006/01/026

published in Journal of High Energy Physics 2006(01), 026 (Springer Nature) · 13 pages, no figures

arxiv created 2006/01/04 · openalex publication_date 2006/01/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

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.

Citations

• New theories in six dimensions and matrix description of M-theory on T5 and
• LLL vs. LLM: Half BPS sector of SYM ≡ quantum Hall system
• The String Dual of a Confining Four-Dimensional Gauge Theory
• BPS geometries and AdS bubbles
• Some half-BPS solutions of M-theory
• 1/2BPS geometries of M2 giant gravitons
• The Supergravity Dual of the BMN Matrix Model
• A matrix big bang
• The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
• Matrix description of M-theory on T4 and T5
• A planar diagram theory for strong interactions
• The world as a hologram
• Toda Fields of SO(3) Hyper-Kahler Metrics and Free Field Realizations
• Fivebranes from gauge theory
• SUPERGRAVITY DESCRIPTION OF FIELD THEORIES ON CURVED MANIFOLDS AND A NO GO THEOREM
• Bubbling orientifolds
• The large N limit of superconformal field theories and supergravity