The conformal bootstrap at finite temperature

A bstract We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for therma...

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Vydané v:The journal of high energy physics Ročník 2018; číslo 10; s. 1 - 71
Hlavní autori: Iliesiu, Luca, Koloğlu, Murat, Mahajan, Raghu, Perlmutter, Eric, Simmons-Duffin, David
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2018
Springer Nature B.V
Springer Berlin
SpringerOpen
Predmet:
Applications programs
Classical and Quantum Gravitation
Conformal Field Theory
Elementary Particles
Field Theories in Higher Dimensions
High energy physics
Mean field theory
Operators (mathematics)
Perturbation theory
Physics
Physics and Astronomy
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Conformal Field Theory
Field Theories in Higher Dimensions
ISSN:1029-8479, 1029-8479
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Abstract A bstract We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O ( N ) model at leading order in 1 /N . Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.
AbstractList A bstract We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O ( N ) model at leading order in 1 /N . Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.
We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O(N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.
We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O ( N ) model at leading order in 1 /N . Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.
Abstract We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O(N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.
ArticleNumber 70
Author Mahajan, Raghu
Simmons-Duffin, David
Koloğlu, Murat
Perlmutter, Eric
Iliesiu, Luca
Author_xml – sequence: 1
  givenname: Luca
  surname: Iliesiu
  fullname: Iliesiu, Luca
  organization: Department of Physics, Princeton University
– sequence: 2
  givenname: Murat
  surname: Koloğlu
  fullname: Koloğlu, Murat
  organization: Walter Burke Institute for Theoretical Physics, Caltech
– sequence: 3
  givenname: Raghu
  surname: Mahajan
  fullname: Mahajan, Raghu
  organization: Department of Physics, Princeton University, School of Natural Sciences, Institute for Advanced Study
– sequence: 4
  givenname: Eric
  surname: Perlmutter
  fullname: Perlmutter, Eric
  email: perl@caltech.edu
  organization: Walter Burke Institute for Theoretical Physics, Caltech
– sequence: 5
  givenname: David
  surname: Simmons-Duffin
  fullname: Simmons-Duffin, David
  organization: Walter Burke Institute for Theoretical Physics, Caltech
BackLink https://www.osti.gov/servlets/purl/1483574$$D View this record in Osti.gov
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SSID ssj0015190
Score 2.6266367
Snippet A bstract We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for...
We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum...
Abstract We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for...
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SubjectTerms Applications programs
Classical and Quantum Gravitation
Conformal Field Theory
Elementary Particles
Field Theories in Higher Dimensions
High energy physics
Mean field theory
Operators (mathematics)
Perturbation theory
Physics
Physics and Astronomy
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
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Title The conformal bootstrap at finite temperature
URI https://link.springer.com/article/10.1007/JHEP10(2018)070
https://www.proquest.com/docview/2122979769
https://www.osti.gov/servlets/purl/1483574
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Volume 2018
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