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Raman, P and Sinha, A (2021) QFT, EFT and GFT. In: Journal of High Energy Physics, 2021 (12).

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Official URL: https://doi.org/10.1007/JHEP12(2021)203


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. © 2021, The Author(s).

Item Type: Journal Article
Publication: Journal of High Energy Physics
Publisher: Springer Science and Business Media Deutschland GmbH
Additional Information: The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 20 Jan 2022 06:54
Last Modified: 20 Jan 2022 06:54
URI: http://eprints.iisc.ac.in/id/eprint/70995

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