Euler-Lagrange equations for high energy actions in QCD and in gravity

L.N Lipatov,V.A Andrianov,V.A Matveev,A.A Andrianov,M.D Fitkevich,V.A Rubakov,V.T Kim

doi:10.1051/epjconf/201612501010

L.N Lipatov, V.A Andrianov + Show 5 more

Open Access

https://doi.org/10.1051/epjconf/201612501010

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Abstract

The high energy scattering in QCD and gravity can be described in terms of reggeized gluons and gravitons, respectively. At N = 4 SUSY the BFKL Pomeron is dual to the reggeized graviton living in the 10-dimensional anti-de-Sitter space. We discuss the corresponding effective actions for reggeized gluon and graviton interactions. The Euler-Lagrange equations for these effective theories are constructed with a variational approach and by using an invariance under the gauge and general coordinate transformations. We discuss their solutions and applications to the calculation of effective Reggeon vertices and trajectories.

Highlights

The hadron scattering amplitudesA(s, t) at high energies√ s and fixed momentum transfers q =√ −t can be presented as sums of the amplitudes Ap with definite signatures p = ±1 Ap(s, t) =a+i∞ d j a−i∞ 2π (−s) j + p s j f jp(t) . (1)The t-channel partial waves f p j (t) have the poles with their positions depending on t f ∼ j
It looks natural to reformulate Quantum Chromodynamics (QCD) and other gauge models in terms of the effective degrees of freedom corresponding to the reggeized gluons
The gluon Regge trajectory and various reggeon couplings in upper orders of perturbation theory can be calculated from the effective action presented in Ref. [6, 7]

Summary

Introduction

Its wave function in QCD and in other field models with the gauge group S U(Nc) satisfies the BFKL equation [3]. It is remarkable, that the equations for the composite states of several reggeized gluons with the color singlet and octet quantum numbers are integrable at large Nc [4, 5]. It looks natural to reformulate QCD and other gauge models in terms of the effective degrees of freedom corresponding to the reggeized gluons. The gluon Regge trajectory and various reggeon couplings in upper orders of perturbation theory can be calculated from the effective action presented in Ref. We consider the Euler-Lagrange equations for the effective actions describing interactions of reggeized gluons and gravitons

Effective action for high energy processes in QCD

Classical equation for the effective action in QCD

Effective action for the high energy gravity

Classical equations for the effective gravity