Analytic Bootstrap of the Veneziano Amplitude

Abstract

We analytically prove, to all orders, that the Veneziano amplitude is the unique outcome of a dual bootstrap based on dispersive sum rules, unitarity, and a small amount of additional stringy input. This stringy input can be either the string monodromy condition or the recently uncovered splitting and hidden-zero conditions. A key ingredient in our proofs is to interpret the dispersive sum rules as sequences of moments. Equally important is the precise incorporation of the extra stringy input into the amplitude ansatz, which makes the analytic bootstrap sufficiently rigid to fix the amplitude uniquely.