"are in fact" is correct and an appropriate phrase to use in written English. You can use "are in fact" when you are offering an explanation or affirming something that is already stated or suggested. For example: "The profits that were expected this year are in fact lower than anticipated."
There are, in fact, fewer.
"You are, in fact, rad".
We are, in fact, patriotic.
Temperatures are, in fact, rising.
Both are in fact very funny.
They are, in fact, the same thing.
Phones are, in fact, carriers of germs.
The games are, in fact, televised.
The meatballs are, in fact, otherworldly good.
Many of them are, in fact, family.
Both are in fact pure Unabomber.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com