Carving out the space of open-string S-matrix

Abstract

In this paper, we explore the open string amplitude’s dual role as a space-time S-matrix and a 2D holomorphic 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 four-dimensional 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 ζ(3)) and 0.2% (of ζ(5)) with respect to the toroidally compactified Type-I 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.

New positivity bounds from full crossing symmetry

“…Moreover, [60] has shown that the determinant of the Hankel matrix formed by a i,0 to a given order is positive. The positivity of this Hankel matrix has found interesting applications in the weak gravity conjecture [61] and string theory amplitudes [62,63]. The optimal positivity of the s derivative amplitudes has been recently sought after in [56] with arc dispersion relations and positive moments, confirming the results of [60] and obtaining optimal bounds truncated to a given order.…”

The EFT-hedron

“…This is very reasonable and is after all precisely what happened in the story of the weak interactions, where the four-fermi interaction was UV completed by W particles, which in turn had bad high-energy growth for the scattering of their longitudinal modes that had to be further cured by the Higgs. It is also interesting to note that imposing just a frisson of extra string properties on the four-particle amplitudesuch as the monodromy relations relating different color channels [32,33] -when combined with the EFT-hedron constraints, do appear to uniquely fix string amplitudes. These observations all suggest a number of fascinating open avenues for further exploration at the intersection of unitarity, causality, analyticity, string theory and the UV/IR connection.…”

Exploring the landscape for soft theorems of nonlinear sigma models

“…It is also well-known that causality enforces positivity constraints on the Wilson coefficients of the chiral Lagrangian [75,76]. This suggests a potential positive geometry which exists in the EFT expansion of NLSM that may be worth investigating as well, using the approach recently developed in [77], including for the closely related Z-theory [78].…”