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TMF, 2005, Volume 144, Number 2, Pages 214–225 (Mi tmf1848)  

This article is cited in 5 scientific papers (total in 5 papers)

Integrability of Generalized (Matrix) Ernst Equations in String Theory

G. A. Alekseev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We elucidate the integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $(d\times d)$-matrix Ernst potentials. These equations arise in string theory as the equations of motion for the truncated bosonic parts of the low-energy effective action for the respective dilaton and $(d\times d)$-matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, a $U(1)$ gauge vector field, and an antisymmetric 3-form field, all depending on only two space-time coordinates. 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 existence conditions for each of these systems of two matrix integrals with appropriate symmetries provide specific (coset) structures of the related matrix variables. We prove that these spectral problems are equivalent to the original field equations, and we envisage an approach for constructing multiparametric families of their solutions.

Keywords: Ernst equations, string gravity, integrability, spectral problems, monodromy

DOI: https://doi.org/10.4213/tmf1848

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English version:
Theoretical and Mathematical Physics, 2005, 144:2, 1065–1074

Bibliographic databases:


Citation: G. A. Alekseev, “Integrability of Generalized (Matrix) Ernst Equations in String Theory”, TMF, 144:2 (2005), 214–225; Theoret. and Math. Phys., 144:2 (2005), 1065–1074

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  • http://mi.mathnet.ru/eng/tmf/v144/i2/p214

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. A. Alekseev, “Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations”, Theoret. and Math. Phys., 143:2 (2005), 720–740  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Gao, YJ, “Inverse scattering method and soliton double solution family for the general symplectic gravity model”, Journal of Mathematical Physics, 49:8 (2008), 083506  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Alekseev, GA, “Integrability of the symmetry reduced bosonic dynamics and soliton generating transformations in the low energy heterotic string effective theory”, Physical Review D, 80:4 (2009), 041901  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    4. Mielke E.W., “Spontaneously broken topological SL(5, R) gauge theory with standard gravity emerging”, Phys Rev D, 83:4 (2011), 044004  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    5. Leigh R.G., Petkou A.C., Petropoulos P.M., Tripathy P.K., “The Geroch Group in Einstein Spaces”, Class. Quantum Gravity, 31:22 (2014), 225006  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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