The Breen Arm was a region of space in the Alpha Quadrant.

When Kotan Pa'Dar was sent on the secret official first contact between the Cardassian Union and the Bajoran government he was listed as being on a charting mission at the Amleth Nebula.

However, he was sure that his family were well aware of this deception and feared that he might have been fighting Tzenkethi or out on the Breen Arm. (DS9 novel: Day of the Vipers)

Presumably, this was the name given to the territory that belonged to the Breen Confederacy.