Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-10-26
Theor.Math.Phys.144:1065-1074,2005; Teor.Mat.Fiz.144:214-225,2005
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, no figures, LaTeX; based on the talk given at the Workshop ``Nonlinear Physics: Theory and Experiment. III'', 24 Jun
Scientific paper
10.1007/s11232-005-0136-4
The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d\times d$-matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion for a truncated bosonic parts of the low-energy effective action respectively for a dilaton and $d\times d$ - matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, U(1) gauge vector field and an antisymmetric 3-form field, all depending on two space-time coordinates only. We construct the corresponding spectral problems based on the overdetermined $2d\times 2d$-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.
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