The field of values of prime-degree characters and Feit’s conjecture

A conjecture by Walter Feit from 1980 states that if \(\chi \) $\chi$ is an irreducible character of a finite group, then the conductor of \(\chi \) $\chi$ is equal to the order of some element of the group. We prove this conjecture for characters of prime degree. As a byproduct, we classify the field of values for these characters, modulo those for quasi-simple groups. Additionally, we prove the same case of a recent related conjecture proposed by the first two authors on the relationship between the cyclotomic deficiency and the degree of an irreducible character.