Operator algebras and conformal field theory
نویسندگان
چکیده
منابع مشابه
Operator Algebras and Conformal Field Theory
We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satis...
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We investigate the quantum conformal algebras of N=2 and N=1 supersymmetric gauge theories. Phenomena occurring at strong coupling are analysed using the Nachtmann theorem and very general, model-independent, arguments. The results lead us to introduce a novel class of conformal field theories, identified by a closed quantum conformal algebra. We conjecture that they are the exact solution to t...
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Two-dimensional conformal quantum field theory (CFT) has inspired an immense amount of mathematics and has interacted with mathematics in very rich ways, in great part through the mathematically dynamic world of string theory. One notable example of this interaction is provided by Verlinde’s conjecture: E. Verlinde (1) conjectured that certain matrices formed by numbers called the “fusion rules...
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In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as " why mathematicians are/should be interested in algebraic quantum field theory " would be equally fitting. Besides a presentation of the framework and the main results of local quantum physics these notes may s...
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Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a deformation of the latter. Alternatively, it can be described as an associative quotient of the algebra given by a modified normal ordered product. We clarify the r...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1993
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02096729