Off-shell BCJ Relation in Nonlinear Sigma Model

Abstract

We investigate relations among tree-level off-shell currents in nonlinear sigma model. Under Cayley parametrization, we propose and prove a general revised BCJ relation for even-point currents. Unlike the on-shell BCJ relation, the off-shell one behaves quite differently from Yang-Mills theory although the algebraic structure is the same. After performing the permutation summation in the revised BCJ relation, the sum is non-vanishing, instead, it equals to the sum of sub-current products with the BCJ coefficients under a specific ordering, which is presented by an explicit formula. Taking on-shell limit, this identity is reduced to the on-shell BCJ relation, and thus provides the full off-shell correspondence of tree-level BCJ relation in nonlinear sigma model.

40 pages, 14 figures

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Cited by in corpus (4)

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• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Non-Abelian gauged supergravities as double copies