Effective action for the Regge processes in gravity

TL;DR

This paper develops a local, covariant effective action for reggeized graviton interactions, explicitly calculates effective currents, and applies these to derive the multi-regge process Lagrangian and graviton Regge trajectory, including supersymmetric effects.

Contribution

It introduces a new formulation of the effective action for reggeized gravitons that is local in rapidity and covariant, and computes explicit currents and trajectories.

Findings

Effective action is local in rapidity and covariant.

Explicit form of effective currents satisfying Hamilton-Jacobi equation.

Reproduction of the multi-regge gravity Lagrangian and graviton Regge trajectory, including supersymmetry.

Abstract

It is shown, that the effective action for the reggeized graviton interactions can be formulated in terms of the reggeon fields $A^{++}$ and $A^{--}$ and the metric tensor $g_{\mu \nu}$ in such a way, that it is local in the rapidity space and has the property of general covariance. The corresponding effective currents $j^{-}$ and $j^{+}$ satisfy the Hamilton-Jacobi equation for a massless particle moving in the gravitational field. These currents are calculated explicitly for the shock wave-like fields and a variation principle for them is formulated. As an application, we reproduce the effective lagrangian for the multi-regge processes in gravity together with the graviton Regge trajectory in the leading logarithmic approximation with taking into account supersymmetric contributions.