The Fu-Yau equation with negative slope parameter

The Fu-Yau equation is an equation introduced by J. Fu and S.T. Yau as a generalization to arbitrary dimensions of an ansatz for the Strominger system. As in the Strominger system, it depends on a slope parameter $\alpha'$. The equation was solved in dimension $2$ by Fu and Yau in two successive papers for $\alpha'>0$, and for $\alpha'<0$. In the present paper, we solve the Fu-Yau equation in arbitrary dimension for $\alpha'<0$. To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater than $2$.