# Causality constraints in CFT There are a few types of causality constraints in CFT: 1. scalar causality constraint - [[2015#Hartman, Jain, Kundu]]: on couplings of scalars such as $(\partial \phi)^4$ 1. [[0493 Conformal collider bounds|Hofman-Maldacena bounds]] - [[2008#Hofman, Maldacena]] - [[2009#Hofman]] - [[2016#Hartman, Jain, Kundu]]: couplings of the stress tensor to light spinning operators; derives [[0417 Averaged null energy condition|ANEC]] from causality; spin-1 and spin-2 cases reduce to a subset of Hofman-Maldacena bounds (ANEC on special states) - [[2016#Hofman, Li, Meltzer, Poland, Rejon-Barrera]] 2. $a=c$ type bounds - derived from bulk - [[2014#Camanho, Edelstein, Maldacena, Zhiboedov]] - derived in CFT - [[KulaxiziParnachevZhiboedov2017]] - [[CostaHansenPenedones2017]] - [[2016#Afkhami-Jeddi, Hartman, Kundu, Tajdini]]: shows that the three parameters in $\langle TTT\rangle$ must be finely tuned to have causality and unitarity 3. shockwave operator bound - [[2017#Afkhami-Jeddi, Hartman, Kundu, Tajdini]] - generalises 1, 2, 3: it can be evaluated in particular states to reproduce each of them ## Related - [[0118 Causality constraints for gravity]]