Two-loop effective potential of O(N)-symmetric scalar QED in 4-ε dimensions

The effective potential of scalar QED is computed analytically up to two loops in the Landau gauge. The result is given in 4-ε dimensions using minimal subtraction and ε-expansions. In three dimensions (ε=1), our calculation is intended to help throw light on unsolved problems of the superconducting phase transition, where critical exponents and the position of the tricritical point have not yet found a satisfactory explanation within the renormalization group approach