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Vertex algebras and conformal field theory models in four dimensions
Author(s) -
Todorov I.
Publication year - 2006
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200510295
Subject(s) - conformal field theory , operator product expansion , conformal symmetry , minkowski space , vertex operator algebra , primary field , conformal map , boundary conformal field theory , vertex (graph theory) , mathematics , modular invariance , conformal anomaly , operator algebra , point (geometry) , pure mathematics , mathematical physics , modular design , algebra over a field , mathematical analysis , current algebra , discrete mathematics , boundary value problem , geometry , computer science , graph , robin boundary condition , jordan algebra , free boundary problem , operating system
The notion of global conformal invariance (GCI) in Minkowski space allows to prove rationality of correlation functions and to extend the concept of vertex algebra to any number D of space‐time dimensions. The case of even D , which includes a conformal stress‐energy tensor with a rational 3‐point function, is of particular interest. Recent progress, reviewed in the talk, includes a full account of Wightman positivity at the 4‐point level for D=4, and a study of modular properties of thermal expectation values of the conformal energy operator.