Description
Higher-derivative quantum corrections are essential ingredients of scalar-tensor effective field theories (EFTs), yet they generically reintroduce the Ostrogradsky ghost instability that the classical theory was designed to avoid. In this talk, we address this tension by establishing a rigorous equivalence between two independent criteria for theoretical consistency. We consider a general DHOST theory including its one-loop quantum corrections and derive consistency conditions through two complementary approaches. First, we obtain a system of differential equations by requiring invariance of the quantum-corrected action under the protective gauge symmetry of the classical theory. Second, we perform a Hamiltonian analysis in the ADM formalism, deriving the primary and secondary constraints necessary to eliminate the ghost degree of freedom. We then show that the resulting symmetry-based and dynamical consistency conditions are mathematically identical.
A distinctive feature of this work is the extensive use of a multi-agent AI system throughout the research process. Whereas AI is currently viewed primarily as a tool for relatively localized tasks such as coding or information retrieval, we investigate its potential role in the broader scientific workflow, including conjecture generation, exploration of theoretical structures, and the identification of nontrivial connections between independent formalisms. This work provides a first step toward assessing whether AI can contribute not only to technical execution but also to the investigation of fundamental questions in theoretical physics.