Equivalence of Meson Scattering Amplitudes in Strong Coupling Lattice and Flat Space String Theory

TL;DR

This paper demonstrates that meson scattering amplitudes derived from strong coupling lattice QCD match those from flat space string theory in the continuum limit, suggesting a deep connection between lattice gauge theories and string models at large N.

Contribution

It establishes a link between lattice strong coupling calculations and flat space string theory for meson scattering, providing evidence for a string-theoretic interpretation of lattice QCD results.

Findings

Lattice meson 4-point functions match worldline formalism results.

Continuum limit of lattice results coincides with Veneziano amplitude.

Holographic arguments support the string theory connection.

Abstract

We consider meson scattering in the framework of the lattice strong coupling expansion. In particular we derive an expression for the 4-point function of meson operators in the planar limit of scalar Chromodynamics. Interestingly, in the naive continuum limit the expression coincides with an independently known result, that of the worldline formalism. Moreover, it was argued by Makeenko and Olesen that (assuming confinement) the resulting scattering amplitude in momentum space is the celebrated expression proposed by Veneziano several decades ago. This motivates us to also use holography in order to argue that the continuum expression for the scattering amplitude is related to the result obtained from flat space string theory. Our results hint that at strong coupling and large-$N_c$ the naive continuum limit of the lattice formalism can be related to a flat space string theory.