What is the genetic background for fast metabolism?
The expression "fast metabolism" is very general and makes the question hard to answer. I will hence answer in the most general sense possible and then just give one example.

Yes, it is most definitely the case that there is genetic variation underlying the variation in metabolic abilities in the human population (btw, this post summarizing the partitioning of phenotypic variation might be helpful to you). For example, Greenlandic Inuits have a series of mutations that affect their ability to digest polyunsaturated fatty acids allowing them to cope with the impressive amount of animal fat that is/was found in their traditional diet (Fumagalli et al., 2015).