The Fu-Yau equation with negative slope parameter

Abstract

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 ${\alpha }^{\prime }$. The equation was solved in dimension $2$ by Fu and Yau in two successive papers for ${\alpha }^{\prime }>0$, and for ${\alpha }^{\prime }<0$. In the present paper, we solve the Fu-Yau equation in arbitrary dimension for ${\alpha }^{\prime }<0$. To our knowledge, these are the first non-trivial solutions of the Fu-Yau equation in any dimension strictly greater than $2$.

30 pages, final version, to appear in Invent. Math

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• The Anomaly flow over Riemann surfaces