# On-shell recursion relations This note will list a few examples of on-shell recursion relations and discuss the general constructibility of theories. ## General constructibility - general refs for constructibility: - [[2007#Benincasa, Cachazo]] - [[2008#Schuster, Toro]] - [[2008#He, Zhang]] - [[2010#Cohen, Elvang, Kiermaier]]: - all-line shift recursion relations - massless or massive; renormalizable or non-renormalizable interactions; with or without supersymmetry - [[2015#Cheung, Shen, Trnka]]: - all amplitudes in non-renormalizable theories without derivative interactions are constructible - with derivative interactions, a subset of amplitudes is constructible - examples: - [[2016#He, Zhang]]: $R^2$, $F^3$, $R^3$, etc.; self-dual and anti-self-dual ## Different recursion relations - [[0058 BCFW]] - [[0515 Inverse soft construction]] - [[0352 CSW relations]] - [[0543 Cachazo-He-Yuan formalism]]