# Finite $N$ corrections to white hot string bits

## Abstract

String bit systems exhibit a Hagedorn transition in the $N$ → ∞ limit. However, there is no phase transition when $N$ is finite (but still large). We calculate two-loop, finite $N$ corrections to the partition function in the low-temperature regime. The Haar measure in the singlet-restricted partition function contributes pieces to loop corrections that diverge as $$\mathcal{O}$$( $N$) when summed over the mode numbers. We study how these divergent pieces cancel each other out when combined. The properly normalized two-loop corrections vanish as $$\mathcal{O}$$( $N$^{–1}) for all temperatures below the Hagedorn temperature. The coefficient of this 1/ $N$ dependence decreases with temperature and diverges at the Hagedorn pole.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Florida, Gainesville, FL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1607572

- Alternate Identifier(s):
- OSTI ID: 1802077

- Grant/Contract Number:
- SC0010296

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 10; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Astronomy & Astrophysics; Physics

## Citation Formats

```
Raha, Sourav. Finite N corrections to white hot string bits. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.106011.
```

```
Raha, Sourav. Finite N corrections to white hot string bits. United States. https://doi.org/10.1103/PhysRevD.100.106011
```

```
Raha, Sourav. Thu .
"Finite N corrections to white hot string bits". United States. https://doi.org/10.1103/PhysRevD.100.106011.
```

```
@article{osti_1607572,
```

title = {Finite N corrections to white hot string bits},

author = {Raha, Sourav},

abstractNote = {String bit systems exhibit a Hagedorn transition in the N → ∞ limit. However, there is no phase transition when N is finite (but still large). We calculate two-loop, finite N corrections to the partition function in the low-temperature regime. The Haar measure in the singlet-restricted partition function contributes pieces to loop corrections that diverge as $\mathcal{O}$(N) when summed over the mode numbers. We study how these divergent pieces cancel each other out when combined. The properly normalized two-loop corrections vanish as $\mathcal{O}$(N–1) for all temperatures below the Hagedorn temperature. The coefficient of this 1/N dependence decreases with temperature and diverges at the Hagedorn pole.},

doi = {10.1103/PhysRevD.100.106011},

journal = {Physical Review D},

number = 10,

volume = 100,

place = {United States},

year = {2019},

month = {11}

}

https://doi.org/10.1103/PhysRevD.100.106011

*Citation information provided by*

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Web of Science

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