# Causality Constraints in Conformal Field Theory

- Institution: CERN
- Department: TH String Theory Seminar
- Speaker: Tom Hartman
- Year: 2015
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3014677)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d-dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators. (Seminar via videolink) .

0:00:00 Slide 1

0:00:40 Slide 2

0:00:54 Slide 3

0:02:02 Slide 4

0:03:29 Slide 5

0:04:10 Slide 6

0:06:08 Slide 7

0:07:08 Slide 8

0:07:36 Slide 9

0:07:59 Slide 10

0:08:05 Slide 11

0:08:45 Slide 12

0:09:46 Slide 13

0:10:41 Slide 14

0:10:58 Slide 15

0:11:08 Slide 16

0:11:18 Slide 17

0:12:03 Slide 18

0:12:36 Slide 19

0:13:22 Slide 20

0:13:55 Slide 21

0:14:14 Slide 22

0:14:22 Slide 23

0:15:45 Slide 24

0:16:34 Slide 25

0:17:13 Slide 26

0:17:42 Slide 27

0:18:05 Slide 28

0:19:44 Slide 29

0:20:23 Slide 30

0:20:37 Slide 31

0:21:32 Slide 32

0:22:47 Slide 33

0:24:02 Slide 34

0:24:54 Slide 35

0:26:06 Slide 36

0:26:42 Slide 37

0:27:42 Slide 38

0:27:53 Slide 39

0:28:39 Slide 40

0:28:54 Slide 41

0:29:27 Slide 42

0:30:04 Slide 43

0:33:09 Slide 44

0:33:20 Slide 45

0:35:11 Slide 46

0:35:50 Slide 47

0:36:17 Slide 48

0:36:30 Slide 49

0:37:07 Slide 50

0:37:33 Slide 51

0:37:49 Slide 52

0:38:51 Slide 53…

## Lectures

1. [Causality Constraints in Conformal Field Theory](https://invisiblenetwork.ai/learn/cern/3014677/11b0db600669), 1 h 26 min (CERN's player)