Worldsheets in Holography: Computing Corrections to the Veneziano Amplitude

TL;DR

This paper develops a holographic method to compute corrections to the Veneziano amplitude, incorporating sub-leading effects and non-linearities in the Regge trajectory of mesonic states.

Contribution

It extends the Makeenko-Olesen approach by formulating a holographic framework for calculating amplitude corrections via a string worldsheet sigma model.

Findings

Provides a prescription for Wilson loop expectation values in strong coupling.

Reformulates the problem as a string worldsheet field theory.

Derives initial corrections using a Feynman diagram approach.

Abstract

We provide a brief summary of a method to calculate improvements to the Veneziano Amplitude, creating sub-leading non-linearities in the Regge trajectory of states. We formulate it as an extension of a computation by Makeenko and Olesen. We begin in a confining gauge theory coupled to matter, rewriting the meson scattering amplitude as a specific path integral over shapes and sizes of closed Wilson loops using the worldline formalism. We then prescribe how to further the computation at strong coupling by employing holography, which provides a prescription for the expectation value of these Wilson loops in strongly coupled regimes. We find that the problem can then be thought of as a computation in an effective field theory of a string worldsheet sigma model, evolving in a broad class of holographic backgrounds. A convenient interaction picture presents itself naturally in this context, allowing us to draw Feynman diagrams corresponding to the first few corrections due to weaker coupling regimes. The answer we find has qualitatively the same features as other endeavours with the same objective.