Love is a central theme of the play because it’s always in question. Unlike the romantic stories of Shakespeare, the foundation of this play is tragedy. Love fails in the end (because the lovers can’t be together), but is upheld by the lovers’ loyalty to each other. The characters’ actions and reactions to one other are all informed by love’s effect on decision-making – specifically, love’s ability to blind people to reason where love is concerned, and the constant fear of losing love.
For Antony, politics is his first love. This is why he can betray Cleopatra so easily for Octavia, and why, at one point, he decides he hates Cleopatra, thinking she’s wronged him politically by joining Caesar.
The love between Antony and Cleopatra is based on power. The lovers could have stayed together in disgrace, or run off, but the real basis of their love for each other is the power each of them holds. Without that power, and the honor implied by it, their relationship means nothing.