### Causality constraints in conformal field theory

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. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators- Publication Date:

- Grant/Contract Number:
- SC0014123

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 5; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Research Org:
- Cornell Univ., Ithaca, NY (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal and W symmetry; field theories in higher dimensions; higher spin symmetry

- OSTI Identifier:
- 1326962

```
Hartman, Thomas, Jain, Sachin, and Kundu, Sandipan.
```*Causality constraints in conformal field theory*. United States: N. p.,
Web. doi:10.1007/JHEP05(2016)099.

```
Hartman, Thomas, Jain, Sachin, & Kundu, Sandipan.
```*Causality constraints in conformal field theory*. United States. doi:10.1007/JHEP05(2016)099.

```
Hartman, Thomas, Jain, Sachin, and Kundu, Sandipan. 2016.
"Causality constraints in conformal field theory". United States.
doi:10.1007/JHEP05(2016)099. https://www.osti.gov/servlets/purl/1326962.
```

```
@article{osti_1326962,
```

title = {Causality constraints in conformal field theory},

author = {Hartman, Thomas and Jain, Sachin and Kundu, Sandipan},

abstractNote = {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. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators},

doi = {10.1007/JHEP05(2016)099},

journal = {Journal of High Energy Physics (Online)},

number = 5,

volume = 2016,

place = {United States},

year = {2016},

month = {5}

}