Anisotropic Asymptotics and High Energy Scattering

TL;DR

This paper explores anisotropic asymptotics in correlation functions of scalar and gauge theories, linking them to high-energy scattering regimes and proposing an effective theory involving conformal theories in different spaces.

Contribution

It introduces the concept of anisotropic asymptotics in four-dimensional theories and relates them to the Regge regime, proposing an effective theory with conformal components.

Findings

Anisotropic asymptotics relate to the Regge scattering regime.

Effective theories involve conformal theories in configuration and momentum space.

Leading terms in Wilson line correlators can be described by reduced effective actions.

Abstract

Recently E.Verlinde and H.Verlinde have suggested an effective two-dimensional theory describing the high-energy scattering in QCD. In this report we attempt to clarify some issues of this suggestion. We consider {\it anisotropic asymptotics} of correlation functions for scalar and gauge theories in four dimensions. Anisotropic asymptotics describe behaviour of correlation functions when some components of coordinates are large as compare with others components. It is occurred that (2+2) anisotropic asymptotics for 4-points functions are related with the well known Regge regime of scattering amplitudes. We study an expansion of correlation functions with respect to the rescaling parameter $\lambda$ over a part of variables (anisotropic $\lambda$-expansion). An effective theory describing the anisotropic limit of free scalar field contains two 2 dim conformal theories. One of them is a conformal theory in configuration space and another one is a conformal theory in momentum space. In some special cases ,in particular for the Wilson line correlators in gauge theories, the leading term of the anisotropic expansion involves only one of the conformal theories and it can be described by an effective theory with an action being a dimensional reduction of the original action.