{"title":"无边界状态下的kontsevic - segal判据约束各向异性","authors":"Thomas Hertog, Oliver Janssen, Joel Karlsson","doi":"10.1103/physrevd.111.046008","DOIUrl":null,"url":null,"abstract":"We show that the Kontsevich-Segal-Witten (KSW) criterion applied to the no-boundary state constrains anisotropic deformations of de Sitter space. We consider squashed S</a:mi>3</a:mn></a:msup></a:math> and <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:msup><c:mi>S</c:mi><c:mn>1</c:mn></c:msup><c:mo>×</c:mo><c:msup><c:mi>S</c:mi><c:mn>2</c:mn></c:msup></c:math> boundaries and find that, in both models, the KSW criterion excludes a significant range of homogeneous but anisotropic configurations. For squashed <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msup><e:mi>S</e:mi><e:mn>3</e:mn></e:msup></e:math> boundaries, the excluded range includes all surface geometries with negative scalar curvature, in line with dS/CFT reasoning. For <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:msup><g:mi>S</g:mi><g:mn>1</g:mn></g:msup><g:mo>×</g:mo><g:msup><g:mi>S</g:mi><g:mn>2</g:mn></g:msup></g:math> boundaries, we find that KSW selects the low-temperature regime of configuration space where the <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:msup><i:mi>S</i:mi><i:mn>1</i:mn></i:msup></i:math> is sufficiently large compared to the <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:msup><k:mi>S</k:mi><k:mn>2</k:mn></k:msup></k:math>. In both models, the KSW criterion renders the semiclassical wave function normalizable, up to one-loop effects. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"9 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kontsevich-Segal criterion in the no-boundary state constrains anisotropy\",\"authors\":\"Thomas Hertog, Oliver Janssen, Joel Karlsson\",\"doi\":\"10.1103/physrevd.111.046008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the Kontsevich-Segal-Witten (KSW) criterion applied to the no-boundary state constrains anisotropic deformations of de Sitter space. We consider squashed S</a:mi>3</a:mn></a:msup></a:math> and <c:math xmlns:c=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><c:msup><c:mi>S</c:mi><c:mn>1</c:mn></c:msup><c:mo>×</c:mo><c:msup><c:mi>S</c:mi><c:mn>2</c:mn></c:msup></c:math> boundaries and find that, in both models, the KSW criterion excludes a significant range of homogeneous but anisotropic configurations. For squashed <e:math xmlns:e=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><e:msup><e:mi>S</e:mi><e:mn>3</e:mn></e:msup></e:math> boundaries, the excluded range includes all surface geometries with negative scalar curvature, in line with dS/CFT reasoning. For <g:math xmlns:g=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><g:msup><g:mi>S</g:mi><g:mn>1</g:mn></g:msup><g:mo>×</g:mo><g:msup><g:mi>S</g:mi><g:mn>2</g:mn></g:msup></g:math> boundaries, we find that KSW selects the low-temperature regime of configuration space where the <i:math xmlns:i=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><i:msup><i:mi>S</i:mi><i:mn>1</i:mn></i:msup></i:math> is sufficiently large compared to the <k:math xmlns:k=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><k:msup><k:mi>S</k:mi><k:mn>2</k:mn></k:msup></k:math>. In both models, the KSW criterion renders the semiclassical wave function normalizable, up to one-loop effects. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>\",\"PeriodicalId\":20167,\"journal\":{\"name\":\"Physical Review D\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":5.3000,\"publicationDate\":\"2025-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review D\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevd.111.046008\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.046008","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Kontsevich-Segal criterion in the no-boundary state constrains anisotropy
We show that the Kontsevich-Segal-Witten (KSW) criterion applied to the no-boundary state constrains anisotropic deformations of de Sitter space. We consider squashed S3 and S1×S2 boundaries and find that, in both models, the KSW criterion excludes a significant range of homogeneous but anisotropic configurations. For squashed S3 boundaries, the excluded range includes all surface geometries with negative scalar curvature, in line with dS/CFT reasoning. For S1×S2 boundaries, we find that KSW selects the low-temperature regime of configuration space where the S1 is sufficiently large compared to the S2. In both models, the KSW criterion renders the semiclassical wave function normalizable, up to one-loop effects. Published by the American Physical Society2025
期刊介绍:
Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including:
Particle physics experiments,
Electroweak interactions,
Strong interactions,
Lattice field theories, lattice QCD,
Beyond the standard model physics,
Phenomenological aspects of field theory, general methods,
Gravity, cosmology, cosmic rays,
Astrophysics and astroparticle physics,
General relativity,
Formal aspects of field theory, field theory in curved space,
String theory, quantum gravity, gauge/gravity duality.