(Quasi-) de Sitter solutions across dimensions and the TCC bound

David Andriot (Laboratoire d’Annecy-le-Vieux de Physique Théorique (LAPTh), CNRS, Université Savoie Mont Blanc (USMB), UMR 5108, 9 Chemin de Bellevue, Annecy, 74940, France) ; Ludwig Horer (Laboratoire d’Annecy-le-Vieux de Physique Théorique (LAPTh), CNRS, Université Savoie Mont Blanc (USMB), UMR 5108, 9 Chemin de Bellevue, Annecy, 74940, France; Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, Vienna, A-1040, Austria)

In this work, we investigate the existence of string theory solutions with a d-dimensional (quasi-) de Sitter spacetime, for 3 ≤ d ≤ 10. Considering classical compactifications, we derive no-go theorems valid for general d. We use them to exclude (quasi-) de Sitter solutions for d ≥ 7. In addition, such solutions are found unlikely to exist in d = 6, 5. For each no-go theorem, we further compute the d-dependent parameter c of the swampland de Sitter conjecture, M p V V c $$ {M}_p\frac{\mid \nabla V\mid }{V}\ge c $$ . Remarkably, the TCC bound c 2 d 1 d 2 $$ c\ge \frac{2}{\sqrt{\left(d-1\right)\left(d-2\right)}} $$ is then perfectly satisfied for d ≥ 4, with several saturation cases. However, we observe a violation of this bound in d = 3. We finally comment on related proposals in the literature, on the swampland distance conjecture and its decay rate, and on the so-called accelerated expansion bound.

{
  "_oai": {
    "updated": "2023-04-26T00:32:35Z", 
    "id": "oai:repo.scoap3.org:74964", 
    "sets": [
      "JHEP"
    ]
  }, 
  "authors": [
    {
      "affiliations": [
        {
          "country": "France", 
          "value": "Laboratoire d\u2019Annecy-le-Vieux de Physique Th\u00e9orique (LAPTh), CNRS, Universit\u00e9 Savoie Mont Blanc (USMB), UMR 5108, 9 Chemin de Bellevue, Annecy, 74940, France", 
          "organization": "Laboratoire d\u2019Annecy-le-Vieux de Physique Th\u00e9orique (LAPTh), CNRS, Universit\u00e9 Savoie Mont Blanc (USMB), UMR 5108"
        }
      ], 
      "surname": "Andriot", 
      "email": "andriot@lapth.cnrs.fr", 
      "full_name": "Andriot, David", 
      "given_names": "David"
    }, 
    {
      "affiliations": [
        {
          "country": "France", 
          "value": "Laboratoire d\u2019Annecy-le-Vieux de Physique Th\u00e9orique (LAPTh), CNRS, Universit\u00e9 Savoie Mont Blanc (USMB), UMR 5108, 9 Chemin de Bellevue, Annecy, 74940, France", 
          "organization": "Laboratoire d\u2019Annecy-le-Vieux de Physique Th\u00e9orique (LAPTh), CNRS, Universit\u00e9 Savoie Mont Blanc (USMB), UMR 5108"
        }, 
        {
          "country": "Austria", 
          "value": "Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, Vienna, A-1040, Austria", 
          "organization": "TU Wien"
        }
      ], 
      "surname": "Horer", 
      "email": "ludwig.horer@tuwien.ac.at", 
      "full_name": "Horer, Ludwig", 
      "given_names": "Ludwig"
    }
  ], 
  "titles": [
    {
      "source": "Springer", 
      "title": "(Quasi-) de Sitter solutions across dimensions and the TCC bound"
    }
  ], 
  "dois": [
    {
      "value": "10.1007/JHEP01(2023)020"
    }
  ], 
  "publication_info": [
    {
      "page_end": "47", 
      "journal_title": "Journal of High Energy Physics", 
      "material": "article", 
      "journal_volume": "2023", 
      "artid": "JHEP01(2023)020", 
      "year": 2023, 
      "page_start": "1", 
      "journal_issue": "1"
    }
  ], 
  "$schema": "http://repo.scoap3.org/schemas/hep.json", 
  "acquisition_source": {
    "date": "2023-04-26T00:30:55.080292", 
    "source": "Springer", 
    "method": "Springer", 
    "submission_number": "7a780660e3c911ed80743e7708eaa62a"
  }, 
  "page_nr": [
    47
  ], 
  "license": [
    {
      "url": "https://creativecommons.org/licenses//by/4.0", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "holder": "The Author(s)", 
      "year": "2023"
    }
  ], 
  "control_number": "74964", 
  "record_creation_date": "2023-01-11T09:30:21.969230", 
  "_files": [
    {
      "checksum": "md5:460376419f1b7d9a354eda73340332ba", 
      "filetype": "xml", 
      "bucket": "b1ea88f8-a581-486d-ad0b-2297b6e8238f", 
      "version_id": "dc195029-8f08-411a-9404-1b1f7213b783", 
      "key": "10.1007/JHEP01(2023)020.xml", 
      "size": 14795
    }, 
    {
      "checksum": "md5:7500184ea1140e77197fae06242e327e", 
      "filetype": "pdf/a", 
      "bucket": "b1ea88f8-a581-486d-ad0b-2297b6e8238f", 
      "version_id": "85373702-2985-4aaa-9f51-20fa70555c7c", 
      "key": "10.1007/JHEP01(2023)020_a.pdf", 
      "size": 819473
    }
  ], 
  "collections": [
    {
      "primary": "Journal of High Energy Physics"
    }
  ], 
  "arxiv_eprints": [
    {
      "categories": [
        "hep-th", 
        "astro-ph.CO", 
        "gr-qc", 
        "hep-ph"
      ], 
      "value": "2208.14462"
    }
  ], 
  "abstracts": [
    {
      "source": "Springer", 
      "value": "In this work, we investigate the existence of string theory solutions with a d-dimensional (quasi-) de Sitter spacetime, for 3 \u2264 d \u2264 10. Considering classical compactifications, we derive no-go theorems valid for general d. We use them to exclude (quasi-) de Sitter solutions for d \u2265 7. In addition, such solutions are found unlikely to exist in d = 6, 5. For each no-go theorem, we further compute the d-dependent parameter c of the swampland de Sitter conjecture,   <math> <msub> <mi>M</mi> <mi>p</mi> </msub> <mfrac> <mrow> <mo>\u2223</mo> <mo>\u2207</mo> <mi>V</mi> <mo>\u2223</mo> </mrow> <mi>V</mi> </mfrac> <mo>\u2265</mo> <mi>c</mi> </math>  $$ {M}_p\\frac{\\mid \\nabla V\\mid }{V}\\ge c $$ . Remarkably, the TCC bound   <math> <mi>c</mi> <mo>\u2265</mo> <mfrac> <mn>2</mn> <msqrt> <mrow> <mfenced> <mrow> <mi>d</mi> <mo>\u2212</mo> <mn>1</mn> </mrow> </mfenced> <mfenced> <mrow> <mi>d</mi> <mo>\u2212</mo> <mn>2</mn> </mrow> </mfenced> </mrow> </msqrt> </mfrac> </math>  $$ c\\ge \\frac{2}{\\sqrt{\\left(d-1\\right)\\left(d-2\\right)}} $$  is then perfectly satisfied for d \u2265 4, with several saturation cases. However, we observe a violation of this bound in d = 3. We finally comment on related proposals in the literature, on the swampland distance conjecture and its decay rate, and on the so-called accelerated expansion bound."
    }
  ], 
  "imprints": [
    {
      "date": "2023-01-09", 
      "publisher": "Springer"
    }
  ]
}
Published on:
09 January 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 1
Pages 1-47
DOI:
https://doi.org/10.1007/JHEP01(2023)020
arXiv:
2208.14462
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: