We explore the correspondence between geometric function theory (GFT) and
    quantum field theory (QFT). The crossing symmetric dispersion relation provides
    the necessary tool to examine the connection between GFT, QFT, and effective
    field theories (EFTs), enabling us to connect with the crossing-symmetric
    EFT-hedron. Several existing mathematical bounds on the Taylor coefficients of
    Typically Real functions are summarized and shown to be of enormous use in
    bounding Wilson coefficients in the context of 2-2 scattering. We prove that
    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) is straightforward and allows
    a systematic exploration. A comparison of our findings obtained using GFT
    techniques and other results in the literature is made. We study both the
    three-channel as well as the two-channel crossing-symmetric cases, the latter
    having some crucial differences. We also consider bound state poles as well as
    massless poles in EFTs. Finally, we consider nonlinear constraints arising from
    the positivity of certain Toeplitz determinants, which occur in the
    trigonometric moment problem.

    Source link


    Leave A Reply