Consistency of gravitational effective field theories

Abstract

Quantum field theories are most pragmatically viewed as effective field theories, accurately describing physics within a finite range of energy or length scales. Effective field theories describe the dynamics of low-energy (IR) degrees of freedom whilst implicitly encoding the influence of their interaction with high-energy (UV) degrees of freedom. The low-energy physics is described by a Wilsonian effective action which can include any operator built out of these IR degrees of freedom, with the details of the UV physics captured by their coupling constants. From a low-energy observer’s perspective, without further input, the values of these coupling constants could take any value, however it is known that if the UV physics satisfies consistency conditions such as unitarity, causality, locality and Lorentz invariance, then the values are strongly restricted by ‘positivity bounds’. The usual derivation of these bounds fails for theories including gravity due to the universal nature of massless graviton exchange. We explore two methods for circumventing these issues: the first involves compactifying space-time to 2 + 1 dimensions, where gravity is non-dynamical, and the second involves assuming a Regge behavior of the scattering amplitude at high energy. In the first, we find that UV consistency conditions applied to minimally coupled quantum electrodynamics lower the cutoff of the EFT dramatically, however we consider that this conclusion may be hindered by issues related to gravity in 2 + 1 dimensions. On the other hand, the second method implies a fascinating connection between IR and UV physics which could imply that UV physics is controlled by the lightest mass scales in the IR.