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Integrability of generalized (matrix) Ernst equations in string theory  G. A. Alekseev
;  Date: 
26 Oct 2004  Journal:  Theor.Math.Phys. 144 (2005) 10651074; Teor.Mat.Fiz. 144 (2005) 214225  Subject:  High Energy Physics  Theory; Exactly Solvable and Integrable Systems  hepth grqc nlin.SI  Abstract:  The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d imes d$matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion for a truncated bosonic parts of the lowenergy effective action respectively for a dilaton and $d imes d$  matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, U(1) gauge vector field and an antisymmetric 3form field, all depending on two spacetime coordinates only. We construct the corresponding spectral problems based on the overdetermined $2d imes 2d$linear systems with a spectral parameter and the universal (i.e. solution independent) structures of the canonical Jordan forms of their matrix coefficients. The additionally imposed conditions of existence for each of these systems of two matrix integrals with appropriate symmetries provide a specific (coset) structures of the related matrix variables. An equivalence of these spectral problems to the original field equations is proved and some approach for construction of multiparametric families of their solutions is envisaged.  Source:  arXiv, hepth/0410246  Services:  Forum  Review  PDF  Favorites 


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