Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes

Diana Vaman; York-Peng Yao

doi:10.1007/JHEP11(2010)028

paper

Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes

arXiv:1007.3475 · doi:10.1007/JHEP11(2010)028

Abstract

Writing the fully color dressed and graviton amplitudes, respectively, as $A =< C ∣ A >=< C ∣ M ∣ N >$ and $A_{g r} =< N ~ ∣ M ∣ N >$ , where $∣ A >$ is a set of Kleiss-Kuijf color-ordered basis, $∣ N >,$ |\tilde N> $an d$ |C> $a r e t h es imi l a r l y or d er e d n u m er a t or s an d co l or coe f f i c i e n t s, w es h o w t ha tt h e p r o p a g a t or ma t r i x$ M $ha s$ (n-3)(n-3)! $in d e p e n d e n t e i g e n v ec t or s$ |λ^0_j> $w i t h z er oe i g e n v a l u e, f or$ n $- p a r t i c l e p r ocesses . T h er es u l t in g e q u a t i o n s$ <λ^0_j|A> = 0 $a r er e l a t i o n s am o n g t h eco l or or d er e d am pl i t u d es . T h e f r ee d o m t os hi f t$ |N> \to |N> +\sum_j f_j|λ^0_j> $an d s imi l a r l y f or$ |\tilde N> $, w h er e$ f_j $a r e$ (n-3)(n-3)! $a r bi t r a r y f u n c t i o n s, e n co d es g e n er a l i z e d g a ug e t r an s f or ma t i o n s . T h ey y i e l d b o t h B C J am pl i t u d e an d K L T r e l a t i o n s, w h e n s u c h f r ee d o mi s a cco u n t e df or . F u r t h er m or e,$ f_j$ can be promoted to the role of effective Lagrangian vertices in the field operator space.

22 pages, JHEP version, Appendix A expanded, one typo fixed

Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes

Abstract

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