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On the positivity of the hypergeometric Veneziano amplitude
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abstract
Recently, an infinite family of one-parameter generalisations of the Veneziano amplitude were bootstrapped using as input assumptions an integer mass spectrum, crossing symmetry, high-energy boundedness, and exchange of finite spins. This new result was dubbed the hypergeometric Veneziano amplitude, with a real-valued deformation parameter r. For concreteness we work in a setup where the lowest-mass state is a tachyon of mass $m^2_0=-1$ and using the partial-wave decomposition and the positivity of said decomposition's coefficients we are able to bound the deformation parameter to $r \geq 0$ and, also, to obtain an upper bound on the number of spacetime dimensions $D \leq 26$, which is the critical dimension of bosonic string theory.
Forward citations
Cited by 3 Pith papers
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Bootstrapping Extremal Scalar Amplitudes With and Without Supersymmetry
The full space of allowed four-point scalar amplitudes is conjectured to be the convex hull of a single scalar amplitude and a one-parameter family of extremal theories, generatable from maximally supersymmetric amplitudes.
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Worldsheet for Generalized Veneziano Amplitudes
A chiral composite linear dilaton worldsheet action reproduces Mandelstam's generalized Veneziano amplitudes and yields new partially crossing-symmetric higher-point and closed-string amplitudes.
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Analytic bootstrap bounds on masses and spins in gravitational and non-gravitational scalar theories
The authors derive 'Sequential Spin and Mass Constraints' for su-symmetric and stu-symmetric four-point amplitudes, claiming any weakly-coupled spectrum must have ordered spins and bounded mass ratios.
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