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The definition of conformal field theory. (English) Zbl 0657.53060

Differential geometrical methods in theoretical physics, Proc. 16th Int. Conf., NATO Adv. Res. Workshop, Como/Italy 1987, NATO ASI Ser., Ser. C 250, 165-171 (1988).
[For the entire collection see Zbl 0646.00009.]
A category \({\mathcal C}\) is introduced with a sequence \(C_0, C_1, C_2,\ldots,\). where \(C_n\) is a disjoint union of \(n\) oriented circles. A morphism \(C_n\to C_m\) is a Riemann surface bounded by the corresponding circles (which geometrically looks like a surface connecting \(n\) circles with \(m\) circles by a surface – or connecting \(n\) closed strings with \(m\) closed strings – in physical application to string theory). The conformal field theory in dimension 2 (one space and one time dimension), which is related to string theory, is then defined as a representation of \({\mathcal C}\) in a complex Hilbert space.

MSC:

53C80 Applications of global differential geometry to the sciences
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
30F99 Riemann surfaces

Citations:

Zbl 0646.00009