On the unitarity and low energy expansion of the Coon amplitude

Abstract

The Coon amplitude is a deformation of the Veneziano amplitude with logarithmic Regge trajectories and an accumulation point in the spectrum, which interpolates between string theory and field theory. With string theory, it is the only other solution to duality constraints explicitly known and it constitutes an important data point in the modern S-matrix bootstrap. Yet, its basics properties are essentially unknown. In this paper we fill this gap and derive the conditions of positivity and the low energy expansion of the amplitude. On the positivity side, we discover that the amplitude switches from a regime where it is positive in all dimensions to a regime with critical dimensions, that connects to the known $d=26,10$ when the deformation is removed. En passant, we find that the Veneziano amplitudes can be extended to massive scalars of masses up to $m^2=1/3$, where it has critical dimension 6.3. On the low-energy side, we compute the first few coupligs of the theory in terms of $q$-deformed analogues of the standard Riemann zeta values of the string expansion. We locate their location in the EFT-hedron, and find agreement with a recent conjecture that theories with accumulation points populate this space. We also discuss their relation to low spin dominance.

9 pages, 6 figures

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• The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness
• UV-Complete Gravity Amplitudes and the Triple Product
• Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon
• Cutting the Coon Amplitude
• On the positivity of Coon amplitude in D=4
• On (Scalar QED) Gravitational Positivity Bounds
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• On the positivity of the hypergeometric Veneziano amplitude
• Non-Forward UV/IR Relations
• Uniqueness Criteria for the Virasoro-Shapiro Amplitude
• Positivity of the Hypergeometric Coon Amplitude
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• Strings from Almost Nothing
• Worldsheet for Generalized Veneziano Amplitudes
• A glimpse into the Ultrametric spectrum