Large N QCD at High Energies as Two-Dimensional Field Theory

TL;DR

This paper explores the connection between high-energy QCD scattering and a two-dimensional sigma-model, deriving an effective theory from lattice Yang-Mills and calculating quantum corrections in the large N limit.

Contribution

It introduces a lattice-based derivation of an effective two-dimensional chiral field model with boundary conditions, linking high-energy QCD to two-dimensional field theories.

Findings

Derived an effective two-dimensional chiral field model from lattice Yang-Mills.

Calculated quantum corrections using character expansion in the large N limit.

Connected high-energy QCD scattering to two-dimensional sigma-model dynamics.

Abstract

Different aspects of the Verlinde and Verlinde relation between high-energy effective scattering in QCD and a two-dimensional sigma-model are discussed. Starting from a lattice version of the truncated 4-dimensional Yang-Mills action we derive an effective theory with non-trivial longitudinal dynamics which has a form of the lattice two-dimensional chiral field model with non-trivial boundary conditions. To get quantum corrections coming from non-trivial longitudinal dynamics to transversal high-energy effective action one has to solve the two-dimensional chiral field model with non-trivial boundary conditions. We do this within an approximation scheme which takes into account one-dimensional excitations. Contributions of the one-dimensional excitations to quantum corrections for the high-energy effective action are calculated in the large N limit using the character expansion method.