Physics

 

Dr. Prashanth Raman
Indian Institute of Science, Bangalore

In this talk we explore the correspondence between geometric function theory (GFT) and quantum field theory (QFT). We begin by introducing a crossing symmetric dispersion relation which provides the necessary tools to examine the connection between GFT, QFT, and effective field theories (EFTs). We then briefly talk about the necessary mathematical results from the GFT of Typically Real functions and how to use them to  bound Wilson coefficients in the context of 2-2 scattering. We discuss why such two-sided bounds on Wilson coefficients are guaranteed to exist quite generally for the fully crossing symmetric situation, numerical implementation of the GFT constraints (Bieberbach-Rogosinski inequalities) and compare with other results known in the literature for both the three-channel as well as the two-channel crossing-symmetric cases, the latter having some crucial differences. We also discuss the bounds for the cases with bound states and massless poles in EFTs. Finally, we discuss the nonlinear constraints that arise from the positivity of certain Toeplitz determinants, which occur in the trigonometric moment problem, enabling us to connect with the crossing-symmetric EFT-hedron.