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Where are HNSW and IVFFLAT indexes for pgvector extension of postgres created and stored?

I am new to postgres and its pgvector extension and might not have clear understanding of the concept. I am running a benchmark against some cloud databases for postgres which support pgvector extension and I am wondering where is the index created; either in RAM or disk, where is index stored and what happens if the memory available is less than index size? Although I have read that pgvector supports creation of index that is greater than memory available but there is no concrete evidence in the documentation. The pgvector extension version is 0.6.0. Two cases come in my mind when the available memory is less than index size:-