The phrase "carry a torch for" means to have a strong and persistent romantic feeling for someone, especially when it is not reciprocated. There are several synonyms for this phrase, including "have a crush on," "be infatuated with," "be smitten with," "be lovesick for," "hold a flame for," and "be pining for." These expressions convey the same sentiment of unrequited love and longing for someone who is not interested in the same way. When we use these phrases, we are expressing a deep emotion that can be challenging to manage, but it also shows our capacity to care for someone genuinely.