The shortest SF story is "Why Booth Did Not Shoot Lincoln" by Ed Wellen; it appeared in Orbit 15, Damon Knight (ed.) in 1974, and is completely blank.
(Does anyone get it??

Maybe it's some sort of pun on 'blank' page/bullet?)
The shortest SF love story ever written is the cleverly titled "The Shortest Science Fiction Love Story Ever Written" by Jeff Renner ("F & SF", March 1964).
It's 9 words long.