The 't Hooft Model As A Hologram

TL;DR

This paper establishes a direct holographic correspondence between the 't Hooft model in 1+1 dimensions and a scalar field in AdS_3, providing a concrete check of the AdS/CFT duality in a simplified setting.

Contribution

It explicitly maps the 't Hooft model's Schroedinger equation to a scalar field in AdS_3, enabling direct verification of the AdS/CFT correspondence in a 2D gauge theory.

Findings

Derived the map between parton-x and AdS_3 radial coordinate.

Checked the AdS/CFT prescription in the conformal limit.

Discussed features of the dual in non-conformal regimes.

Abstract

We consider the 3d dual of 1+1 dimensional large-N_c QCD with quarks in the fundamental representation, also known as the 't Hooft model. 't Hooft solved this model by deriving a Schroedinger equation for the wavefunction of a parton inside the meson. In the scale-invariant limit, we show how this equation is related by a transform to the equation of motion for a scalar field in AdS_3. We thus find an explicit map between the `parton-x' variable and the radial coordinate of AdS_3. This direct map allows us to check the AdS/CFT prescription from the 2d side. We describe various features of the dual in the conformal limit and to the leading order in conformal symmetry breaking, and make some comments on the 3d theory in the fully non-conformal regime.