Carving out the Space of Open-String S-matrix

TL;DR

This paper investigates the dual role of open string amplitudes as both space-time S-matrices and 1D CFT correlators, revealing how Virasoro symmetry and monodromy constraints shape the space of consistent EFT couplings, with implications for string amplitude uniqueness.

Contribution

It demonstrates how Virasoro symmetry emerges at the boundary of consistent factorization and how monodromy relations constrain EFT couplings, suggesting the open superstring amplitude is uniquely determined by geometric intersections.

Findings

Virasoro symmetry appears at the boundary of consistent factorization.

Monodromy relations impose algebraic constraints on EFT couplings.

The intersection of monodromy plane and EFThedron tightly constrains string couplings.

Abstract

In this paper, we explore the open string amplitude's dual role as a space-time S-matrix and a 1D CFT correlation function. We pursue this correspondence in two directions. First, beginning with a general disk integrand dressed with a Koba-Nielsen factor, we demonstrate that exchange symmetry for the factorization residue of the amplitude forces the integrand to be expandable on SL(2,R) conformal blocks. Furthermore, positivity constraints associated with unitarity imply the SL(2,R) blocks must come in linear combinations for which the Virasoro block emerges at the "kink" in the space of solutions. In other words, Virasoro symmetry arises at the boundary of consistent factorization. Next, we consider the low energy EFT description, where unitarity manifests as the EFThedron in which the couplings must live. The existence of a worldsheet description implies, through the Koba-Nielsen factor, monodromy relations which impose algebraic identities amongst the EFT couplings. We demonstrate at finite derivative order that the intersection of the "monodromy plane" and the EFThedron carves out a tiny island for the couplings, which continues to shrink as the derivative order is increased. At the eighth derivative order, on a three-dimensional monodromy plane, the intersection fixes the width of this island to around 1.5$\%$ (of $\zeta(3)$) and 0.2$\%$ (of $\zeta(5)$) with respect to the super string answer. This leads us to conjecture that the four-point open superstring amplitude can be completely determined by the geometry of the intersection of the monodromy plane and the EFThedron.