Effective field theory in light of relative entropy

Abstract

Abstract We study constraints on the effective field theory (EFT) from the relative entropy between two theories: we refer to these as target and reference theories. The consequence of the non-negativity of the relative entropy is investigated by choosing some reference theories for a given target theory. We consider the target and reference theories described by field theories, quantum mechanical models, etc. It is found that the constraints on EFTs, e.g., the single massless scalar field with the dimension-eight operator, and SMEFT dimension-eight bosonic operators, arise when the higher-derivative operators are generated by the interaction between heavy and light fields. In particular, the constraints on the SMEFT dimension-eight bosonic operators with the SU(N) and SU(n) gauge fields, and the operator quartics in the Higgs are newly studied, and some stronger bounds than the unitarity and causality considerations are derived. The constraints on Einstein-Maxwell theory with higher-derivative operators from the non-negativity of relative entropy are also investigated. The constraints on such EFTs from the relative entropy hold under an assumption that perturbative corrections from the interaction involving higher-derivative operators of light fields are not dominant in the EFTs. The consequence of this study on the weak gravity conjecture and the second law of thermodynamics is also discussed.