Massless limit of massive self-interacting vector fields

TL;DR

This paper investigates the massless limit of massive self-interacting vector fields, revealing that the limit is not smooth due to classical and quantum pathologies, including unitarity violation at two loops.

Contribution

It demonstrates the failure of the massless limit in self-interacting vector theories both classically and quantum mechanically, highlighting the limitations of the Vainshtein mechanism.

Findings

Massless limit is not smooth at classical and quantum levels.

Unitarity is violated at two-loop order.

Vainshtein mechanism fails beyond strong-coupling scale.

Abstract

We study massive self-interacting vector field theories with mass added ``by hand". We show that the massless limit of the quartic self-interacting vector field theory is not smooth. Pathological behavior of the theory is not limited only at the classical level, even at the quantum level unitarity is violated at the two-loop. Using the Vainshtein mechanism, we show that it fails beyond the strong-coupling scale and hence a massless limit is not smooth even in quantum theory.