Among them, Isabella Stewart Gardner Museum director Anne Hawley, Institute of Contemporary Art director Jill Medvedow, and Museum of Fine Arts director Malcolm Rogers have led their institutions for a total of 58 years. They’ve raised hundreds of millions of dollars, led massive museum construction projects, and expanded staff and programming. But running a major Boston museum remains a challenge, they say, particularly in a city that provides few resources (re: cash). That’s why all three directors are closely monitoring John Connolly and Marty Walsh’s battle for City Hall. What do they hope to see from the next mayor of Boston? We gathered Hawley, Medvedow, and Rogers at the MFA recently to talk about city politics, their missions, and more. Here are excerpts.