Conformal Field Theories in Fractional Dimensions

We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predi...

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Detalles Bibliográficos
Autores principales: El-Showk, Sheer, Paulos, Miguel, Poland, David, Rychkov, Slava, Simmons-Duffin, David, Vichi, Alessandro
Lenguaje:eng
Publicado: 2013
Materias:
Particle Physics - Theory
Acceso en línea:https://dx.doi.org/10.1103/PhysRevLett.112.141601
http://cds.cern.ch/record/1602361
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author El-Showk, Sheer
Paulos, Miguel
Poland, David
Rychkov, Slava
Simmons-Duffin, David
Vichi, Alessandro
author_facet El-Showk, Sheer
Paulos, Miguel
Poland, David
Rychkov, Slava
Simmons-Duffin, David
Vichi, Alessandro
author_sort El-Showk, Sheer
collection CERN
description We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.
id cern-1602361
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2013
record_format invenio
spelling cern-16023612021-10-22T05:50:40Zdoi:10.1103/PhysRevLett.112.141601http://cds.cern.ch/record/1602361engEl-Showk, SheerPaulos, MiguelPoland, DavidRychkov, SlavaSimmons-Duffin, DavidVichi, AlessandroConformal Field Theories in Fractional DimensionsParticle Physics - TheoryWe study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.<p>We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of <inline-formula><mml:math display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> and compare these to calculations of <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> theory in the <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>ϵ</mml:mi></mml:mrow></mml:math></inline-formula> expansion.</p>We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of phi^4 theory in the epsilon-expansion.arXiv:1309.5089CERN-PH-TH-2013-219CERN-PH-TH-2013-219oai:cds.cern.ch:16023612013-09-19
spellingShingle Particle Physics - Theory
El-Showk, Sheer
Paulos, Miguel
Poland, David
Rychkov, Slava
Simmons-Duffin, David
Vichi, Alessandro
Conformal Field Theories in Fractional Dimensions
title Conformal Field Theories in Fractional Dimensions
title_full Conformal Field Theories in Fractional Dimensions
title_fullStr Conformal Field Theories in Fractional Dimensions
title_full_unstemmed Conformal Field Theories in Fractional Dimensions
title_short Conformal Field Theories in Fractional Dimensions
title_sort conformal field theories in fractional dimensions
topic Particle Physics - Theory
url https://dx.doi.org/10.1103/PhysRevLett.112.141601
http://cds.cern.ch/record/1602361
work_keys_str_mv AT elshowksheer conformalfieldtheoriesinfractionaldimensions
AT paulosmiguel conformalfieldtheoriesinfractionaldimensions
AT polanddavid conformalfieldtheoriesinfractionaldimensions
AT rychkovslava conformalfieldtheoriesinfractionaldimensions
AT simmonsduffindavid conformalfieldtheoriesinfractionaldimensions
AT vichialessandro conformalfieldtheoriesinfractionaldimensions

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