The band American Authors, which performed during the NHL Winter Classic at Gillette Stadium and at the AFC Championship Game in Denver, has signed on to entertain at the Polartec Big Air at Fenway event next week. The skiing and snowboarding competition at the ballpark runs Feb. 11-12. The band, best known for the single “Best Day of My Life,’’ will perform after the skiing finals that Friday. Also on the lineup for the icy festivities are DJ Master Millions, who’ll warm up the crowd each night, and the Boston band Bad Rabbits, which will perform after Thursday’s snowboarding finals.