Inflation Models in Supergravity with a Running Spectral Index

The first year Wilkinson Microwave Anisotropy Probe data favors primordial adiabatic fluctuation with a running spectral index with n_s > 1 on a large scale and n_s < 1 on a smaller scale. The model building of inflation that predicts perturbations with such a spectrum is a challenge. We give sensible particle physics models in supergravity that accommodate the desired running of the spectral index and discuss a method to discriminate those models.