2026 Theses Doctoral

A Journey Across Scales: Causality, Symmetry, and Unitarity in Effective Field Theory

McLoughlin, Daniel C.

Effective field theories provide a universal framework for describing physics at a given energy scale without requiring complete knowledge of the underlying microscopic dynamics. However, their predictive power depends on our ability to constrain or determine the parameters that govern them.

This dissertation investigates how three fundamental physical principles — causality, symmetry, and unitarity — applied to appropriately chosen physical variables, dictate the structure of effective field theories across three widely separated physical regimes. At the cosmological scale, we construct explicit shockwave solutions in de Sitter spacetime, carefully account for the stretching of the Penrose diagram in response to positive-energy matter, and establish a rigorous diagnostic for causality violations. Applying this criterion to higher-derivative gravitational couplings, we derive new bounds on the low-energy effective theory, providing a de Sitter analogue of known flat and anti-de Sitter causality constraints. At the astrophysical scale, we address the naturalness puzzle posed by the vanishing of static tidal Love numbers of four-dimensional black holes.

By identifying hidden symmetries in the static perturbation equations through an appropriate choice of field variables, we provide a unified geometric explanation for this vanishing across perturbations of different spin and trace its consequences into the worldline effective field theory. At the subatomic scale, we propose that the structure of renormalization group flow is fixed by the unitarity of the Scattering Matrix. Working in massless scalar field theory and organizing the perturbative expansion by loop and logarithmic order, we show that the non-linear identities imposed by the optical theorem reproduce the recursion relations ordinarily derived from the renormalization group equation, without reference to Feynman diagrams or counterterms.

Taken together, these results illustrate that foundational physical mandates, when applied to the appropriate degrees of freedom, provide powerful constraints on effective field theories from cosmological to subatomic scales.