Does unique email in user table violate normal forms?
To extend the hole idea why index doesn't matter
A indexed filed onlys describes that every row is unique, but this doewsn'z means that it is dependend from other columns than the promary key

A relation is in third normal form if there is no transitive dependency for non-prime attributes

following this definition, it still stands an indexed email field is  dependent on the primary key and does not depend on other columns it is non transitively dependent
Which means that it correspnds teh 3NF