Songfacts®:

• Like many Interpol songs, the title doesn't appear in the lyric. The song is about a breakup, with the singer appearing conflicted between love and hated for his ex.
  
  "PDA" is an initialism that stands for "Public Display of Affection," which could relate to his anger when he sees her with another guy.
• Even by Interpol standards, the lyric is rather opaque, and was made even more incomprehensible with the line, "Sleep tight, grim rite, we have two hundred couches where you can sleep tonight." The band didn't print the lyrics with the album, so fans struggled to figure out exactly what lead singer Paul Banks was saying. They eventually posted the lyrics on their website to help out their ESL fans in Europe; a "grim rite" is an unfortunate ritual - much different than a "grim right," which would be the right to do something grim. In this context, the line refers to the girl's proclivity for sleeping around - that's her "grim rite."
• A track from Interpol's first album, "PDA" became one of their most popular live cuts and got decent airplay on American modern rock radio. The video, directed by Christopher Mills, was the band's first.