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

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

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf1848
• https://doi.org/10.4213/tmf1848
• http://mi.mathnet.ru/eng/tmf/v144/i2/p214

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
4. Mielke E.W., “Spontaneously broken topological SL(5, R) gauge theory with standard gravity emerging”, Phys Rev D, 83:4 (2011), 044004
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
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