The phrase "have not" is commonly used to indicate a lack of possession or action. However, there are several synonyms that can be used interchangeably depending on the context. Some alternatives to "have not" include "do not have," "lack," "are without," "have no," "do without," "are deprived of," and "are in want of." Each of these words carries a slightly different connotation and can help to add variety and nuance to your writing. Using synonyms can also help to avoid repetition and make your writing more engaging and interesting to read.