Theory HEP Seminar

Positivity Constraints on EFTs and Geometric function theory

Prashanth Raman

Indian Institute of Science

In this talk, we shall look at the implications of crossing symmetry, locality, and unitarity in the UV on low-energy efts. We will begin by looking at 2-2 scattering amplitudes with identical external particles and introduce a crossing symmetric dispersive representation (CSDR) of the amplitude that makes full (s,t,u)-crossing symmetry manifest, unlike the usual fixed-t dispersion relations. Though the CSDR makes crossing symmetry manifest, locality is lost and has to be restored by demanding that certain spurious singularities cancel in the low energy expansion of the amplitude leading to locality constraints.

For massive external particles, the CSDR and unitarity make a certain analyticity property of the amplitude called typically-realness manifest and enables us to use techniques from the geometric function theory (GFT) of typically-real functions to show that the low energy Wilson coefficients have to be o(1) numbers and that the space of these Wilson coefficients is finite.

We then discuss the extension to weakly coupled efts with massless spinning particles and the corresponding bounds on Wilson coefficients using GFT techniques. We show that the locality constraints imply an infinite linear system of equations that the partial wave moments of any local theory need to satisfy. Finally, we show that additionally imposing linear unitarity (positivity of partial waves), naturally leads to the phenomenon of low-spin dominance (LSD).