Pervasiveness of the breakdown of self-interacting vector field theories

Abstract

Various groups recently argued that self-interacting vector field theories lack a well-defined time evolution when the field grows to large amplitudes, which has drastic consequences for models in gravity and high energy theory. Such field amplitudes can be a result of an external driving mechanism, or occur intrinsically, due to large values of the field and its derivatives in the initial data. This brings a natural question: is small amplitude initial data guaranteed to evolve indefinitely in these theories in the absence of an outside driving term? We answer this question in the negative, demonstrating that arbitrarily low amplitude initial data can still lead to the breakdown of the theory. Namely, ingoing spherically symmetric wave packets in more than one spatial dimensions grow as an inverse power of the radius, and their amplitudes can generically reach high enough values where time evolution ceases to exist. This simple example further establishes the pervasiveness of the pathology of self-interacting vector field theories.

arXiv comment5 pages, 1 figure. Published version in PRD

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• Conformally and Disformally Coupled Vector field Models of Dark Energy
• Scalaroca stars: coupled scalar-Proca solitons
• Treatments and placebos for the pathologies of effective field theories
• Loss of hyperbolicity and tachyons in generalized Proca theories
• Aspects of time evolution in $p$-form field theories
• Black hole destabilization via trapped quasi-normal modes
• Internal symmetry to the rescue: well-posed 1+1 evolution of self-interacting vector fields