Harmonic analysis of 2d CFT partition functions

A bstract We apply the theory of harmonic analysis on the fundamental domain of SL(2 , ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(...

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Published inThe journal of high energy physics Vol. 2021; no. 9; pp. 1 - 51
Main Authors Benjamin, Nathan, Collier, Scott, Fitzpatrick, A. Liam, Maloney, Alexander, Perlmutter, Eric
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 27.09.2021
Springer Nature B.V
Springer
Springer Nature
SpringerOpen
Subjects
Bosons
Classical and Quantum Gravitation
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Conformal and W Symmetry
Conformal Field Theory
Decomposition
Eigenvectors
Elementary Particles
Field Theories in Lower Dimensions
Fourier analysis
Harmonic analysis
High energy physics
High Energy Physics - Theory
Operators (mathematics)
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Spectral theory
String Theory
Field Theories in Lower Dimensions
Conformal Field Theory
Conformal and W Symmetry
spectral
operator: local
moduli space
dimension: 2
analysis: harmonic
operator: spectrum
field theory: conformal
anti-de Sitter
gravitation
partition function
SL
Z
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Abstract A bstract We apply the theory of harmonic analysis on the fundamental domain of SL(2 , ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2 , ℤ), and of target space moduli space O ( c, c ; ℤ)\ O ( c, c ; ℝ)/ O ( c ) × O ( c ). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS 3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
AbstractList We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2, ℤ), and of target space moduli space O(c, c; ℤ)\O(c, c; ℝ)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS$_{3}$ gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
We apply the theory of harmonic analysis on the fundamental domain of SL(2 , ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2 , ℤ), and of target space moduli space O ( c, c ; ℤ)\ O ( c, c ; ℝ)/ O ( c ) × O ( c ). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS 3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
Abstract We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2, ℤ), and of target space moduli space O(c, c; ℤ)\O(c, c; ℝ)/O(c)× O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
A bstract We apply the theory of harmonic analysis on the fundamental domain of SL(2 , ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2 , ℤ), and of target space moduli space O ( c, c ; ℤ)\ O ( c, c ; ℝ)/ O ( c ) × O ( c ). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS 3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space ℍ/SL(2, ℤ), and of target space moduli space O(c, c; ℤ)\O(c, c; ℝ)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
We apply the theory of harmonic analysis on the fundamental domain of SL(2, Z) to partition functions of two-dimensional conformal field theories. We decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space H/SL(2, Z), and of target space moduli space O(c, c; Z)\O(c, c; R)/O(c)×O(c). This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to AdS3 gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.
ArticleNumber 174
Author Benjamin, Nathan
Collier, Scott
Maloney, Alexander
Perlmutter, Eric
Fitzpatrick, A. Liam
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  fullname: Benjamin, Nathan
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  givenname: Scott
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  fullname: Collier, Scott
  organization: Princeton Center for Theoretical Science, Princeton University
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  givenname: A. Liam
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  fullname: Fitzpatrick, A. Liam
  organization: Department of Physics, Boston University
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  givenname: Alexander
  surname: Maloney
  fullname: Maloney, Alexander
  organization: Department of Physics, McGill University
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  givenname: Eric
  surname: Perlmutter
  fullname: Perlmutter, Eric
  organization: Institut de Physique Théorique, CEA Saclay, CNRS, Walter Burke Institute for Theoretical Physics, Caltech
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https://www.osti.gov/servlets/purl/1851504$$D View this record in Osti.gov
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Issue 9
Keywords Field Theories in Lower Dimensions
Conformal Field Theory
Conformal and W Symmetry
spectral
operator: local
moduli space
dimension: 2
analysis: harmonic
operator: spectrum
field theory: conformal
anti-de Sitter
gravitation
partition function
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Z
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Snippet A bstract We apply the theory of harmonic analysis on the fundamental domain of SL(2 , ℤ) to partition functions of two-dimensional conformal field theories....
We apply the theory of harmonic analysis on the fundamental domain of SL(2 , ℤ) to partition functions of two-dimensional conformal field theories. We...
We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We decompose...
We apply the theory of harmonic analysis on the fundamental domain of SL(2, Z) to partition functions of two-dimensional conformal field theories. We decompose...
Abstract We apply the theory of harmonic analysis on the fundamental domain of SL(2, ℤ) to partition functions of two-dimensional conformal field theories. We...
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SubjectTerms Bosons
Classical and Quantum Gravitation
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Conformal and W Symmetry
Conformal Field Theory
Decomposition
Eigenvectors
Elementary Particles
Field Theories in Lower Dimensions
Fourier analysis
Harmonic analysis
High energy physics
High Energy Physics - Theory
Operators (mathematics)
Partitions (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Spectral theory
String Theory
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Title Harmonic analysis of 2d CFT partition functions
URI https://link.springer.com/article/10.1007/JHEP09(2021)174
https://www.proquest.com/docview/2577604188
https://hal.science/hal-03315948
https://www.osti.gov/servlets/purl/1851504
https://doaj.org/article/557e54cd850f4d138eccaeeac9d6b703
Volume 2021
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