Positivity of the hypergeometric Veneziano amplitude

Abstract

Recently, an infinite family of one-parameter generalizations 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>m</a:mi><a:mn>0</a:mn><a:mn>2</a:mn></a:msubsup><a:mo>=</a:mo><a:mo>−</a:mo><a:mn>1</a:mn></a:math> and using the partial-wave decomposition and the positivity of said decomposition’s coefficients we are able to bound the deformation parameter to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>r</c:mi><c:mo>≥</c:mo><c:mn>0</c:mn></c:math> and, also, to obtain an upper bound on the number of spacetime dimensions <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:mo>≤</e:mo><e:mn>26</e:mn></e:math>, which is the critical dimension of bosonic string theory. Published by the American Physical Society 2024

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