arts vs field of study

arts and field of study both are nouns.

Word	Noun	Adjective	Verb	Adverb
arts	Yes	No	No	No
field of study	Yes	No	No	No

As nouns, field of study is a hypernym of arts; that is, field of study is a word with a broader meaning than arts:

arts: studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)
field of study: a branch of knowledge

Other hypernyms of arts include bailiwick, discipline, field, study, subject, subject area, subject field.

arts (noun)	field of study (noun)
studies intended to provide general knowledge and intellectual skills (rather than occupational or professional skills)	a branch of knowledge