Regge Regime in QCD and Asymmetric Lattice Gauge Theory

Abstract

We study the Regge regime of QCD as a special regime of lattice gauge theory on an asymmetric lattice. This lattice has a spacing $a_0 $ in the longitudinal direction and a spacing $a_t $ in the transversal direction. The limit $\frac{a_{0}}{a_{t}} \to 0$ corresponds to correlation functions with small longitudinal and large transversal coordinates, i.e. large $s$ and small $t$. On this lattice the longitudinal dynamics is described by the usual two-dimensional chiral field in finite volume and the transversal dynamics is emerged through an effective interaction of boundary terms of the longitudinal dynamics. The effective interaction depends crucially on the spectrum of the two-dimensional chiral field. Massless exitations produce an effective 2-dimensional action which is different from the action recently proposed by H.Verlinde and E.Verlinde. Massive exitations give raise to an effective action located on the contour in the longitudinal plane.