Effective field theory in light of relative entropy

TL;DR

This paper explores how the non-negativity of relative entropy imposes constraints on effective field theories, aligning with known positivity bounds and providing insights into quantum gravity and thermodynamics.

Contribution

It introduces a novel approach using relative entropy to derive constraints on EFTs, connecting information theory with field theory and gravity.

Findings

Constraints from relative entropy are consistent with positivity bounds.

Higher-derivative operators generated by heavy-light interactions satisfy these constraints.

Implications for the weak gravity conjecture and thermodynamics are discussed.

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 involving 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 $SU(N)$ gauge bosonic operators, are consistent with the positivity bounds from the unitarity and causality when the higher-derivative operators are generated by the interaction between heavy and light fields. 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.