### Abstract

We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic 2- dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, “asymptotic fragility”. Asymptotically fragile flows do not originate from a UV fixed point.

Original language | English (US) |
---|---|

Pages (from-to) | 1-35 |

Number of pages | 35 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 9 |

DOIs | |

State | Published - Sep 27 2012 |

### Fingerprint

### Keywords

- 2D gravity
- Bethe ansatz
- Bosonic strings
- Exact S-matrix

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(9), 1-35. https://doi.org/10.1007/JHEP09(2012)133

**Solving the simplest theory of quantum gravity.** / Dubovsky, Sergei; Flauger, Raphael; Gorbenko, Victor.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2012, no. 9, pp. 1-35. https://doi.org/10.1007/JHEP09(2012)133

}

TY - JOUR

T1 - Solving the simplest theory of quantum gravity

AU - Dubovsky, Sergei

AU - Flauger, Raphael

AU - Gorbenko, Victor

PY - 2012/9/27

Y1 - 2012/9/27

N2 - We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic 2- dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, “asymptotic fragility”. Asymptotically fragile flows do not originate from a UV fixed point.

AB - We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic 2- dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, “asymptotic fragility”. Asymptotically fragile flows do not originate from a UV fixed point.

KW - 2D gravity

KW - Bethe ansatz

KW - Bosonic strings

KW - Exact S-matrix

UR - http://www.scopus.com/inward/record.url?scp=84878921123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878921123&partnerID=8YFLogxK

U2 - 10.1007/JHEP09(2012)133

DO - 10.1007/JHEP09(2012)133

M3 - Article

AN - SCOPUS:84878921123

VL - 2012

SP - 1

EP - 35

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

ER -