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The first-order bosonic field equations of the D-dimensional effective low energy theory which describes the massless background coupling of the D-dimensional fully Higgsed heterotic string are derived. [ABSTRACT FROM AUTHOR]

After explicitly constructing the symmetric space sigma model Lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism, we derive the field equations of the theory. [ABSTRACT FROM AUTHOR]

The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws. [ABSTRACT FROM AUTHOR]

We have applied the method of dualization to construct the coset realization of the bosonic sector of the $\mathcal{N}=2$, D = 6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan–Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the nonlinear coset construction. [ABSTRACT FROM AUTHOR]