"Burning for" is commonly used to express strong desire or passion towards something. There are several synonyms that can effectively communicate this sentiment such as yearning, craving, hungering, thirsting, longing, and pining. "Yearning" implies a deep emotional longing for something one cannot have or obtain easily. "Craving" is a more intense desire, often used in relation to a specific object or experience. "Hungering" and "thirsting," on the other hand, suggest a desperate need or desire for something. "Longing" and "pining" are both used to express a strong desire or yearning for something that is absent. All of these synonyms capture the intensity of the desire or passion one may have towards something they are "burning for".