Quantum stability of the phase transition in rigid QED

Rigid QED is a renormalizable generalization of Feynmanʹs space-time action characterized by the addition of the curvature of the worldline (rigidity). We have recently shown that a phase transition occurs in the leading approximation of the large N limit. The disordered phase essentially coincides with ordinary QED, while the ordered phase is a new theory. We have further shown that both phases of the quantum theory are free of ghosts and tachyons. In this letter, we study the first subleading quantum corrections leading to the renormalized mass gap equation. Our main result is that the phase transition does indeed survive these quantum fluctuations.