Duality Symmetry in Momentum Frame

TL;DR

This paper extends Siegel's action for chiral p-forms to higher dimensions and investigates their self-duality in the momentum space, revealing non-local Lagrangians and algebraic solutions for dual tensors.

Contribution

It generalizes Siegel's action to D=2(p+1) dimensions and explores self-duality of chiral p-forms in momentum space, including non-local Lagrangians and algebraic dual tensor relations.

Findings

Self-duality of chiral p-forms in momentum space is established.

Non-local Lagrangians in momentum space are derived.

Algebraic solutions for dual tensor relations are provided.

Abstract

Siegel's action is generalized to the D=2(p+1) (p even) dimensional space-time. The investigation of self-duality of chiral p-forms is extended to the momentum frame, using Siegel's action of chiral bosons in two space-time dimensions and its generalization in higher dimensions as examples. The whole procedure of investigation is realized in the momentum space which relates to the configuration space through the Fourier transformation of fields. These actions correspond to non-local Lagrangians in the momentum frame. The self-duality of them with respect to dualization of chiral fields is uncovered. The relationship between two self-dual tensors in momentum space, whose similar form appears in configuration space, plays an important role in the calculation, that is, its application realizes solving algebraically an integral equation.