TY - JOUR

T1 - Correspondence between strings in the Hagedorn phase and asymptotically de Sitter space

AU - Brustein, Ram

AU - Medved, A. J.M.

N1 - Funding Information:
We would like to thank Sunny Itzhaki, Volodya Kazakov, Kyriakos Papadodimas, Riccardo Rattazzi, Misha Shaposhnikov, Marko Simonovic, Gabriele Veneziano, Sasha Zhiboedov, and, in particular, Toni Riotto and Yoav Zigdon for useful discussions and suggestions. We would also like to thank Thomas Hertog, Heliudson de Oliveira Bernardo, and Kostas Skenderis for clarifying discussions on their work. The research of R. B. was supported by the Israel Science Foundation Grant No. 1294/16. The research of AJMM received support from an NRF Evaluation and Rating Grant No. 119411 and a Rhodes Discretionary Grant No. RD38/2019. R. B. thanks the TH division, CERN where part of this research was conducted. AJMM thanks Ben Gurion University for their hospitality during his visit.
Publisher Copyright:
© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

PY - 2020/10/6

Y1 - 2020/10/6

N2 - A correspondence between closed strings in their high-temperature Hagedorn phase and asymptotically de Sitter (dS) space is established. We identify a thermal, conformal field theory (CFT) whose partition function is, on the one hand, equal to the partition function of closed, interacting, fundamental strings in their Hagedorn phase yet is, on the other hand, also equal to the Hartle-Hawking (HH) wave function of an asymptotically dS universe. The Lagrangian of the CFT is a functional of a single scalar field, the condensate of a thermal scalar, which is proportional to the entropy density of the strings. The correspondence has some aspects in common with the anti-de Sitter/CFT correspondence, as well as with some of its proposed analytic continuations to a dS/CFT correspondence, but it also has some important conceptual and technical differences. The equilibrium state of the CFT is one of maximal pressure and entropy, and it is at a temperature that is above but parametrically close to the Hagedorn temperature. The CFT is valid beyond the regime of semiclassical gravity and thus defines the initial quantum state of the dS universe in a way that replaces and supersedes the HH wave function. Two-point correlation functions of the CFT scalar field are used to calculate the spectra of the corresponding metric perturbations in the asymptotically dS universe and, hence, cosmological observables in the postinflationary epoch. Similarly, higher-point correlation functions in the CFT should lead to more complicated cosmological observables.

AB - A correspondence between closed strings in their high-temperature Hagedorn phase and asymptotically de Sitter (dS) space is established. We identify a thermal, conformal field theory (CFT) whose partition function is, on the one hand, equal to the partition function of closed, interacting, fundamental strings in their Hagedorn phase yet is, on the other hand, also equal to the Hartle-Hawking (HH) wave function of an asymptotically dS universe. The Lagrangian of the CFT is a functional of a single scalar field, the condensate of a thermal scalar, which is proportional to the entropy density of the strings. The correspondence has some aspects in common with the anti-de Sitter/CFT correspondence, as well as with some of its proposed analytic continuations to a dS/CFT correspondence, but it also has some important conceptual and technical differences. The equilibrium state of the CFT is one of maximal pressure and entropy, and it is at a temperature that is above but parametrically close to the Hagedorn temperature. The CFT is valid beyond the regime of semiclassical gravity and thus defines the initial quantum state of the dS universe in a way that replaces and supersedes the HH wave function. Two-point correlation functions of the CFT scalar field are used to calculate the spectra of the corresponding metric perturbations in the asymptotically dS universe and, hence, cosmological observables in the postinflationary epoch. Similarly, higher-point correlation functions in the CFT should lead to more complicated cosmological observables.

UR - http://www.scopus.com/inward/record.url?scp=85093510074&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.102.086002

DO - 10.1103/PhysRevD.102.086002

M3 - Article

AN - SCOPUS:85093510074

VL - 102

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 8

M1 - 086002

ER -