political sphere vs arena

political sphere and arena both are nouns.

Word	Noun	Adjective	Verb	Adverb
political sphere	Yes	No	No	No
arena	Yes	No	No	No

As nouns, arena is a hypernym of political sphere; that is, arena is a word with a broader meaning than political sphere:

Other hypernyms of political sphere include area, domain, field, orbit, sphere.

political sphere (noun)	arena (noun)
a sphere of intense political activity	a playing field where sports events take place
	a large structure for open-air sports or entertainments
	the central area of an ancient Roman amphitheater where contests and spectacles were held; especially an area that was strewn with sand
	a particular environment or walk of life