The antonyms for the phrase "art connected with" would be anything that is not related to creative expression or aesthetics. This could include tasks or professions that are more technical or analytical in nature, such as engineering, mathematics, or accounting. It may also encompass activities that are considered more athletic or physical, like sports or construction work. The opposite of art could therefore encompass any profession or pastime that doesn't involve making something beautiful or expressive. However, it's worth noting that the definition of "art" varies widely depending on cultural and historical contexts, so the definition of its antonym is also subject to interpretation.