# A magnetically induced quantum critical point in holography

## Abstract

Here, we investigate quantum critical points in a 2+1 dimensional gauge theory at finite chemical potential χ and magnetic field B. The gravity dual is based on 4D N = 2 Fayet-Iliopoulos gauged supergravity and the solutions we consider — that are constructed analytically — are extremal, dyonic, asymptotically *AdS _{4}* black-branes with a nontrivial radial profile for the scalar field. We discover a line of second order fixed points at B = B

_{c}(χ) between the dyonic black brane and an extremal “thermal gas” solution with a singularity of good-type, according to the acceptability criteria of Gubser. The dual field theory is a strongly coupled nonconformal field theory at finite charge and magnetic field, related to the ABJM theory deformed by a triple trace operator Φ

^{3}. This line of fixed points might be useful in studying the various strongly interacting quantum critical phenomena such as the ones proposed to underlie the cuprate superconductors. We also find curious similarities between the behaviour of the VeV under B and that of the quark condensate in 2+1 dimensional NJL models.

- Authors:

- KU Leuven, Leuven (Belgium)
- Utrecht Univ., Utrecht (The Netherlands)
- Columbia Univ., New York, NY (United States)

- Publication Date:

- Research Org.:
- Columbia Univ., New York, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1360129

- Grant/Contract Number:
- SC0011941

- Resource Type:
- Journal Article: 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: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; AdS-CFT correspondence; black holes in string theory; gauge-gravity correspondence; holography and condensed matter physics (AdS/CMT)

### Citation Formats

```
Gnecchi, A., Gursoy, U., Papadoulaki, O., and Toldo, C..
```*A magnetically induced quantum critical point in holography*. United States: N. p., 2016.
Web. doi:10.1007/JHEP09(2016)090.

```
Gnecchi, A., Gursoy, U., Papadoulaki, O., & Toldo, C..
```*A magnetically induced quantum critical point in holography*. United States. doi:10.1007/JHEP09(2016)090.

```
Gnecchi, A., Gursoy, U., Papadoulaki, O., and Toldo, C.. Thu .
"A magnetically induced quantum critical point in holography". United States.
doi:10.1007/JHEP09(2016)090. https://www.osti.gov/servlets/purl/1360129.
```

```
@article{osti_1360129,
```

title = {A magnetically induced quantum critical point in holography},

author = {Gnecchi, A. and Gursoy, U. and Papadoulaki, O. and Toldo, C.},

abstractNote = {Here, we investigate quantum critical points in a 2+1 dimensional gauge theory at finite chemical potential χ and magnetic field B. The gravity dual is based on 4D N = 2 Fayet-Iliopoulos gauged supergravity and the solutions we consider — that are constructed analytically — are extremal, dyonic, asymptotically AdS4 black-branes with a nontrivial radial profile for the scalar field. We discover a line of second order fixed points at B = Bc(χ) between the dyonic black brane and an extremal “thermal gas” solution with a singularity of good-type, according to the acceptability criteria of Gubser. The dual field theory is a strongly coupled nonconformal field theory at finite charge and magnetic field, related to the ABJM theory deformed by a triple trace operator Φ3. This line of fixed points might be useful in studying the various strongly interacting quantum critical phenomena such as the ones proposed to underlie the cuprate superconductors. We also find curious similarities between the behaviour of the VeV under B and that of the quark condensate in 2+1 dimensional NJL models.},

doi = {10.1007/JHEP09(2016)090},

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

number = 9,

volume = 2016,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}

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