Analytic Bootstrap of the Veneziano Amplitude

TL;DR

This paper provides an all-orders analytic proof that the Veneziano amplitude is uniquely determined by a dual bootstrap approach incorporating dispersive sum rules, unitarity, and specific stringy conditions.

Contribution

It introduces a rigorous analytic bootstrap method that uniquely fixes the Veneziano amplitude using dispersive sum rules and stringy input conditions.

Findings

Proves the uniqueness of the Veneziano amplitude to all orders.

Shows the importance of dispersive sum rules as sequences of moments.

Demonstrates how stringy conditions rigidify the amplitude ansatz.

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.