Entropy constraints on effective field theory

Abstract

In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that the positivity bounds on some operators of the effective field theory, e.g., dimension-eight term of a single massless scalar field, the Standard Model Effective Field Theory dimension-eight $SU(N)$ gauge bosonic operators, and higher-derivative operators in the Einstein-Maxwell theory, generated by interactions between heavy and light degrees of freedom can be derived by the non-negativity of relative entropy. For such effective field theories, we prove that the interactions increase thermodynamic entropy at a fixed charge and an extremal point of energy, which is intimately connected with the extremality relations of black holes exhibiting Weak-Gravity-Conjecture. These arguments are applicable when corrections from the interactions involving higher-derivative operators of light fields are not dominant in the effective field theories. The entropy constraint is a consequence of the Hermiticity of Hamiltonian, and any theory violating the non-negativity of entropy would not respect the second law of thermodynamics.

arXiv comment31 pages, 2 figures; several explanations were modified, and detailed calculations and explanations were added

References in corpus (18)

• The String Landscape, Black Holes and Gravity as the Weakest Force
• The Role of Relative Entropy in Quantum Information Theory
• Causality, Analyticity and an IR Obstruction to UV Completion
• Entropy production as correlation between system and reservoir
• Higher-order corrections to mass-charge relation of extremal black holes
• Weak Gravity Conjecture from Unitarity and Causality
• Proof of the Weak Gravity Conjecture from Black Hole Entropy
• Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity
• Consistency of the Standard Model Effective Field Theory
• Generalization of the Second Law for a Nonequilibrium Initial State
• Causality, Unitarity, and the Weak Gravity Conjecture
• A Universal Relation Between Corrections to Entropy and Extremality
• Higher derivative corrections to Kerr black hole thermodynamics
• Entropy Bounds on Effective Field Theory from Rotating Dyonic Black Holes
• Relative entropy and the RG flow
• Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture
• Field Theory Entropy, the $H$-theorem and the Renormalization Group
• The effective action for gauge bosons

Cited by in corpus (4)

• Running Love Numbers and the Effective Field Theory of Gravity
• Perturbative unitarity bounds from momentum-space entanglement
• Entanglement features in scattering mediated by heavy particles
• Relative Entropy and Mutual Information in Gaussian Statistical Field Theory