"debate arena" is correct and usable in written English.
You can use it to refer to a space dedicated to debates, either virtually or in-person. For example, "The debate arena was full of students eager to participate on the day of the tournament."
Municipal Art Society: 'Atlantic Yards: Urban Debate, Arena Debut' (Saturday) This tour covers the history and future development of the Brooklyn neighborhoods surrounding the Barclays Center.
A sense of unease spread across the debate arena at the Citadel in South Carolina last night when Mike Gravel, the 77-year-old former senator from Alaska, responded to a question by saying, "The Democratic Party used to stand for the ordinary working man.
But fluency in the debate arena will not be sufficient to kick him upstairs.
Rubio brings two important skills to the debate arena: a talent for deflecting incoming attacks and an alertness to his opportunities.
Professor Warren had her best night in the debate arena thus far, delivering a performance that was focused, confident and energetic.
What the party would be left with is a select group of elitists who have the visibility, name-recognition and wealth to fuel their own campaigns outside of the debate arena.
Rationality, by this yardstick (and irrationality too, but we'll get to that) is nothing more or less than a servant of the hard-wired compulsion to triumph in the debating arena.
This might let a graphic dose of shutdown reality waft up to the hermetic debating arena on Capitol Hill, but Mayor Gray prefers to let city life go on as usual.
Data collection, another intensely debated arena, seems to be the need of the hour for government bodies to analyse, improve and facilitate evidence-based interventions to reduce fatalities.
Hence their attempts to deflect attention from the issue itself and shift the debate into the arena of abuse.
Khan will appear at the BBC's EU referendum debate at Wembley arena on Tuesday opposite Boris Johnson.
