In this dazzling new dance musical, which opened Thursday night at the Marquis Theater, Ms. Tharp deploys a stage full of brilliant performers to heighten the theatrical allure of ballroom dance, complementing the immortal appeal of Sinatra’s singing with movement that captures the underlying emotional tensions in it. The yearning to connect and the impulse toward flight — those contradictory verities of romantic entanglement — take sharp visceral form in Ms. Tharp’s fast, flashing, remarkably intricate dances.