QFT, EFT and GFT

Abstract

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.

v3: 95 pages, 18 figures; improvement in presentation, version to appear in JHEP, v4: minor typo in appendix fixed

References in corpus (9)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Sharp Boundaries for the Swampland
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Where is String Theory?
• AdS Bulk Locality from Sharp CFT Bounds
• Quantum field theory and the Bieberbach conjecture
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Distributions in CFT II. Minkowski Space
• Dispersion Formulas in QFTs, CFTs, and Holography

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