UV completions of Chern-Simons gravity

Dynamical Chern-Simons (dCS) gravity is a four-dimensional parity-violating extension of general relativity. The standard mechanism to obtain this extension predicts negligible observational effects due to a large decay constant f close to the scale of grand unified theories. Here, we present two constructions of dCS that permit much smaller decay constants, ranging from sub-eV to Planck scales. That is, we show that, in the same manner as axions, dCS gravity can arise from both spontaneous and dynamical symmetry breaking. In either case, the angular part of a complex scalar field develops a pseudoscalar Yukawa interaction with a set of fermions. In the former case, the complex scalar field is a fundamental particle, and in the latter case, it is a bound state of short-wavelength fermion modes arising from strong four-Fermi self-interactions. Due to the Yukawa interaction, loop corrections with gravitons then realize a linear coupling between the angular pseudoscalar and the gravitational Chern-Simons term. The strength of this coupling is set by the Yukawa coupling constant divided by the fermion mass. Therefore, since fermions with small masses are ideal, we identify neutrinos as promising candidates. For example, if a neutrino has a mass m_ and the Yukawa coupling is order unity, the dCS decay constant can be smaller than f10^3m_. We discuss other potential choices for fermions and give two examples of four-Fermi UV completions.