Vivid to Farrah Abraham -- Keep Your Mouth Shut ... OR ELSE

Vivid Entertainment execs are FREAKED OUT at Farrah Abraham's upcoming book about the sex tape industry ... and they've fired off a letter demanding that she keep her trap shut.

Vivid honcho Steve Hirsch has a lot to lose if Farrah blabs about how the porn company courts and signs celeb talent. Hirsch believes his trade secrets are worth millions ... but only if they remain secret.

Farrah's book -- "Celebrity Sex Tape" -- is loosely based on her experience in the porn biz which ended in "Back Door Teen Mom."

We're told Hirsch worries Farrah could blow the lid on the way her tape was made with porn star James Deen. It was marketed as a sex tape, but it's pretty apparent it was Hirsch's brainchild.

In Hirsch's letter ... he notes Farrah signed a confidentiality agreement and she can't hide behind thinly-veiled fiction.