Gap is chasing relevance with beauty, handbags, and a dream team of seasoned luxury executives. But the real story is one of classic retail tension: fix the core problem, or chase the bright, shiny new thing? Here’s a simple question with big implications: Can Gap reinvent itself by chasing relevance, or is it just distracting itself from the hard work of fixing the core business? Gap Inc. CEO Richard Dickson arrived with a Midas Touch reputation from the Mattel and Barbie whirlwind.