IAS Amplitudes Group Meeting

Abstract: What is the mathematical question about the S-matrix to which string amplitudes are the answer? In this talk, I will show that both the four-point Veneziano and Virasoro-Shaprio amplitudes, along with the string spectrum itself, are the unique solutions to an analytically solvable bootstrap problem. Relaxing the bootstrap conditions, we will discover deformations of both the open and closed string, in the open case finding the hypergeometric and Coon amplitudes and more, and in the closed case reproducing remarkable extremal amplitudes that appear in bottom-up studies of positivity.