Counting and construction of holomorphic primary fields in free CFT4 from rings of functions on Calabi-Yau orbifolds

A bstract Counting formulae for general primary fields in free four dimensional conformal field theories of scalars, vectors and matrices are derived. These are specialised to count primaries which obey extremality conditions defined in terms of the dimensions and left or right spins (i.e. in terms...

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Published in:	The journal of high energy physics Vol. 2017; no. 8; pp. 1 - 48
Main Authors:	de Mello Koch, Robert, Rabambi, Phumudzo, Rabe, Randle, Ramgoolam, Sanjaye
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017 Springer Nature B.V SpringerOpen
Subjects:	AdS-CFT Correspondence Classical and Quantum Gravitation Conformal Field Theory Counting Elementary Particles Field theory Functions (mathematics) High energy physics Mathematical analysis Matrix algebra Matrix methods Physics Physics and Astronomy Polynomials Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory Scalars Space-Time Symmetries String Theory AdS-CFT Correspondence Conformal Field Theory Space-Time Symmetries
ISSN:	1029-8479, 1029-8479
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Abstract	A bstract Counting formulae for general primary fields in free four dimensional conformal field theories of scalars, vectors and matrices are derived. These are specialised to count primaries which obey extremality conditions defined in terms of the dimensions and left or right spins (i.e. in terms of relations between the charges under the Cartan subgroup of SO(4, 2)). The construction of primary fields for scalar field theory is mapped to a problem of determining multi-variable polynomials subject to a system of symmetry and differential constraints. For the extremal primaries, we give a construction in terms of holomorphic polynomial functions on permutation orbifolds, which are shown to be Calabi-Yau spaces.
AbstractList	Abstract Counting formulae for general primary fields in free four dimensional conformal field theories of scalars, vectors and matrices are derived. These are specialised to count primaries which obey extremality conditions defined in terms of the dimensions and left or right spins (i.e. in terms of relations between the charges under the Cartan subgroup of SO(4, 2)). The construction of primary fields for scalar field theory is mapped to a problem of determining multi-variable polynomials subject to a system of symmetry and differential constraints. For the extremal primaries, we give a construction in terms of holomorphic polynomial functions on permutation orbifolds, which are shown to be Calabi-Yau spaces. A bstract Counting formulae for general primary fields in free four dimensional conformal field theories of scalars, vectors and matrices are derived. These are specialised to count primaries which obey extremality conditions defined in terms of the dimensions and left or right spins (i.e. in terms of relations between the charges under the Cartan subgroup of SO(4, 2)). The construction of primary fields for scalar field theory is mapped to a problem of determining multi-variable polynomials subject to a system of symmetry and differential constraints. For the extremal primaries, we give a construction in terms of holomorphic polynomial functions on permutation orbifolds, which are shown to be Calabi-Yau spaces.
ArticleNumber	77
Author	Rabambi, Phumudzo Rabe, Randle de Mello Koch, Robert Ramgoolam, Sanjaye
Author_xml	– sequence: 1 givenname: Robert surname: de Mello Koch fullname: de Mello Koch, Robert email: robert@neo.phys.wits.ac.za organization: National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of Witwatersrand – sequence: 2 givenname: Phumudzo surname: Rabambi fullname: Rabambi, Phumudzo organization: National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of Witwatersrand – sequence: 3 givenname: Randle surname: Rabe fullname: Rabe, Randle organization: National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of Witwatersrand – sequence: 4 givenname: Sanjaye surname: Ramgoolam fullname: Ramgoolam, Sanjaye organization: National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical Physics, University of Witwatersrand, Centre for Research in String Theory, School of Physics and Astronomy, Queen Mary University of London
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Snippet	A bstract Counting formulae for general primary fields in free four dimensional conformal field theories of scalars, vectors and matrices are derived. These... Abstract Counting formulae for general primary fields in free four dimensional conformal field theories of scalars, vectors and matrices are derived. These are...
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SubjectTerms	AdS-CFT Correspondence Classical and Quantum Gravitation Conformal Field Theory Counting Elementary Particles Field theory Functions (mathematics) High energy physics Mathematical analysis Matrix algebra Matrix methods Physics Physics and Astronomy Polynomials Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory Scalars Space-Time Symmetries String Theory
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Title	Counting and construction of holomorphic primary fields in free CFT4 from rings of functions on Calabi-Yau orbifolds
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