A new report says that Massachusetts cultural groups pump more than a billion dollars a year into the economy. But the “cultural sector is losing its luster as a tourist destination, and it is in danger of losing ground as a cultural hub as well. Theaters and historic homes are crumbling, and vital museums and arts centers are struggling to pay for basic repairs, maintenance, and expansion planned, the report found. Yet Massachusetts is one of the few culture-rich regions of the country that provides no steady support for capital improvements.”