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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Veröffentlicht in:The journal of high energy physics Jg. 2017; H. 8; S. 1 - 48
Hauptverfasser: de Mello Koch, Robert, Rabambi, Phumudzo, Rabe, Randle, Ramgoolam, Sanjaye
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017
Springer Nature B.V
SpringerOpen
Schlagworte:
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
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP08(2017)077