Strominger's equations
In heterotic string theory, the Strominger's equations are the set of equations that are necessary and sufficient conditions for spacetime supersymmetry. It is derived by requiring the 4-dimensional spacetime to be maximally symmetric, and adding a warp factor on the internal 6-dimensional manifold. Consider a metric formula_1 on the real 6-dimensional internal manifold "Y" and a Hermitian metric "h" on a vector bundle "V". The equations are: These equations imply the usual field equations, and thus are the only equations to be solved. However, there are topological obstructions in obtaining the solutions to  the equations; In case "V" is the tangent bundle formula_18 and formula_1 is Kähler, we can obtain a solution of these equations by taking the Calabi–Yau metric on formula_20 and formula_18. Once the solutions for the Strominger's equations are obtained, the warp factor formula_22, dilaton formula_23 and the background flux "H", are determined by