## Bootstrapping 3D fermions with global symmetries

## Abstract

We study the conformal bootstrap for 4-point functions of fermions < ψ _{i} ψ _{j} ψ _{k} ψ _{ℓ} > in parity-preserving 3d CFTs, where ψ _{i} transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.

- Authors:

- Princeton Univ., NJ (United States). Joseph Henry Lab.
- Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics. Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group
- Yale Univ., New Haven, CT (United States). Dept. of Physics
- Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Inst. for Advanced Study, Princeton, NJ (United States); Princeton Univ., NJ (United States); Yale Univ., New Haven, CT (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF); Simons Foundation (United States)

- OSTI Identifier:
- 1494081

- Grant/Contract Number:
- AC02-05CH11231; SC0009988; PHY-1418069; PHY-1350180; 488653; 488651; 488657

- Resource Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N expansion; conformal and W symmetry; conformal field theory; global symmetries

### Citation Formats

```
Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., and Simmons-Duffin, David. Bootstrapping 3D fermions with global symmetries. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)036.
```

```
Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., & Simmons-Duffin, David. Bootstrapping 3D fermions with global symmetries. United States. doi:10.1007/jhep01(2018)036.
```

```
Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., and Simmons-Duffin, David. Tue .
"Bootstrapping 3D fermions with global symmetries". United States. doi:10.1007/jhep01(2018)036. https://www.osti.gov/servlets/purl/1494081.
```

```
@article{osti_1494081,
```

title = {Bootstrapping 3D fermions with global symmetries},

author = {Iliesiu, Luca and Kos, Filip and Poland, David and Pufu, Silviu S. and Simmons-Duffin, David},

abstractNote = {We study the conformal bootstrap for 4-point functions of fermions < ψ i ψ j ψ k ψ ℓ > in parity-preserving 3d CFTs, where ψ i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.},

doi = {10.1007/jhep01(2018)036},

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

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}

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