Generalized mirror symmetry and trace anomalies

We consider the compactification of M-theory on X-7 with Betti numbers (b(0), b(1), b(2), b(3), b(3), b(2), b(1), b(0)) and define a generalized mirror symmetry (b(0), b(1), b(2), b(3)) -> (b(0), b(1), b(2) - rho/2, b(3) + rho/2) under which rho equivalent to 7b(0) - 5b(1) + 3b(2) - b(3) changes sign. Generalized self-mirror theories with rho = 0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with N >= 4 and supergravity plus matter with N <= 4.