Changes in Trace Anomalies along RG Flows and S-Matrix Bootstrap Bounds

In this talk, I will present how scattering amplitudes involving
background dilaton and graviton fields can serve as powerful probes of
trace anomalies along four-dimensional renormalization group (RG) flows.
By coupling these fields to quantum field theory degrees of freedom while
preserving the Weyl anomaly structure, I will show that dilaton-dilaton
and graviton-dilaton scattering amplitudes directly encode the changes in
trace anomaly coefficients between ultraviolet (UV) and infrared (IR)
conformal field theories (CFTs). This framework will be tested through
explicit perturbative examples, demonstrating its robustness across
controlled settings. I will then describe how these ideas can be extended
non-perturbatively using the S-matrix bootstrap, which leverages
analyticity, unitarity, crossing symmetry, and Regge behavior to place
universal lower bounds on the UV a-anomaly coefficient for gapped RG flows
arising from relevant deformations of UV CFTs. This study provides a
concrete step toward addressing a fundamental question in quantum field
theory: for a given massive QFT, what is the space of possible UV CFTs
that can flow to it?