English

Integrability of generalized (matrix) Ernst equations in string theory

High Energy Physics - Theory 2009-11-10 v2 General Relativity and Quantum Cosmology Exactly Solvable and Integrable Systems

Abstract

The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric d×dd\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×dd\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×2d2d\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.

Keywords

Cite

@article{arxiv.hep-th/0410246,
  title  = {Integrability of generalized (matrix) Ernst equations in string theory},
  author = {G. A. Alekseev},
  journal= {arXiv preprint arXiv:hep-th/0410246},
  year   = {2009}
}

Comments

15 pages, no figures, LaTeX; based on the talk given at the Workshop ``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004, Gallipoli (Lecce), Italy. Minor typos, language and references corrections. To be published in the proceedings in Theor. Math. Phys

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