# Thermal phase transition in Yang-Mills matrix model

## Abstract

We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU(N) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and this hinders progress in understanding the nature of the black hole/black string topology change from the gauge/gravity duality perspective. On the one hand, previous works considered the deconfinement transition consistent with two transitions which are of second and third order. On the other hand, evidence for a first order transition was put forward more recently. We perform high-statistics lattice Monte Carlo simulations at large N and small lattice spacing to establish that the transition is really of first order. Our findings flag a warning that the required large-N and continuum limit might not have been reached in earlier publications, and that was the source of the discrepancy. Moreover, our detailed results confirm the existence of a new partially deconfined phase which describes non-uniform black strings via the gauge/gravity duality. This phase exhibits universal features already predicted in quantum field theory.

- Authors:

- Univ. of Jena (Germany)
- Univ. of Regensburg, Universitatsstrasse (Germany)
- Univ. of Southampton (United Kingdom)
- Arithmer Inc., Tokyo (Japan); RIKEN, Saitama (Japan)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1592028

- Report Number(s):
- LLNL-JRNL-782380

Journal ID: ISSN 1029-8479; 978069

- Grant/Contract Number:
- AC52-07NA27344

- 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: 2020; 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; Gauge-gravity correspondence; Lattice Quantum Field Theory; M(atrix) Theories

### Citation Formats

```
Bergner, Georg, Bodendorfer, Norbert, Hanada, Masanori, Rinaldi, Enrico, Schäfer, Andreas, and Vranas, Pavlos. Thermal phase transition in Yang-Mills matrix model. United States: N. p., 2020.
Web. doi:10.1007/JHEP01(2020)053.
```

```
Bergner, Georg, Bodendorfer, Norbert, Hanada, Masanori, Rinaldi, Enrico, Schäfer, Andreas, & Vranas, Pavlos. Thermal phase transition in Yang-Mills matrix model. United States. doi:10.1007/JHEP01(2020)053.
```

```
Bergner, Georg, Bodendorfer, Norbert, Hanada, Masanori, Rinaldi, Enrico, Schäfer, Andreas, and Vranas, Pavlos. Fri .
"Thermal phase transition in Yang-Mills matrix model". United States. doi:10.1007/JHEP01(2020)053. https://www.osti.gov/servlets/purl/1592028.
```

```
@article{osti_1592028,
```

title = {Thermal phase transition in Yang-Mills matrix model},

author = {Bergner, Georg and Bodendorfer, Norbert and Hanada, Masanori and Rinaldi, Enrico and Schäfer, Andreas and Vranas, Pavlos},

abstractNote = {We study the bosonic matrix model obtained as the high-temperature limit of two-dimensional maximally supersymmetric SU(N) Yang-Mills theory. So far, no consensus about the order of the deconfinement transition in this theory has been reached and this hinders progress in understanding the nature of the black hole/black string topology change from the gauge/gravity duality perspective. On the one hand, previous works considered the deconfinement transition consistent with two transitions which are of second and third order. On the other hand, evidence for a first order transition was put forward more recently. We perform high-statistics lattice Monte Carlo simulations at large N and small lattice spacing to establish that the transition is really of first order. Our findings flag a warning that the required large-N and continuum limit might not have been reached in earlier publications, and that was the source of the discrepancy. Moreover, our detailed results confirm the existence of a new partially deconfined phase which describes non-uniform black strings via the gauge/gravity duality. This phase exhibits universal features already predicted in quantum field theory.},

doi = {10.1007/JHEP01(2020)053},

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

number = 1,

volume = 2020,

place = {United States},

year = {2020},

month = {1}

}

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