  In multi-field inflation models, correlated adiabatic and isocurvature
fluctuations are produced and in addition to the usual adiabatic fluctuation
with a spectral index n_ad1 there is another adiabatic component with a
spectral index n_ad2 generated by entropy perturbation during inflation, if the
trajectory in the field space is curved. Allowing n_ad1 and n_ad2 to vary
independently we find that the WMAP data favour models where the two adiabatic
components have opposite spectral tilts. This leads naturally to a running
adiabatic spectral index. The WMAP data with a prior n_iso < 1.84 for the
isocurvature spectral index gives fiso < 0.84 for the isocurvature fraction of
the initial power spectrum at k_0 = 0.05 Mpc^{-1}. We also comment on a
degeneration between the correlation component and the optical depth tau.
Moreover, the measured low quadrupole in the TT angular power could be achieved
by a strong negative correlation, but then one would need a large tau to fit
the TE spectrum.
