Classification of Local Conformal Nets. Case c < 1

We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs of A-D_{2n}-E_{6,8} Dynkin diagrams such that the difference of their Coxeter numbers is equal to 1. We first identify the nets generated by irreducible representations of the Virasoro algebra for c<1 with certain coset nets. Then, by using the classification of modular invariants for the minimal models by Cappelli-Itzykson-Zuber and the method of alpha-induction in subfactor theory, we classify all local irreducible extensions of the Virasoro nets for c<1 and infer our main classification result. As an application, we identify in our classification list certain concrete coset nets studied in the literature.Comment: 30 pages, LaTeX2

Twistors, CFT and Holography

According to one of many equivalent definitions of twistors a (null) twistor is a null geodesic in Minkowski spacetime. Null geodesics can intersect at points (events). The idea of Penrose was to think of a spacetime point as a derived concept: points are obtained by considering the incidence of twistors. One needs two twistors to obtain a point. Twistor is thus a ``square root'' of a point. In the present paper we entertain the idea of quantizing the space of twistors. Twistors, and thus also spacetime points become operators acting in a certain Hilbert space. The algebra of functions on spacetime becomes an operator algebra. We are therefore led to the realm of non-commutative geometry. This non-commutative geometry turns out to be related to conformal field theory and holography. Our construction sheds an interesting new light on bulk/boundary dualities.Comment: 21 pages, figure

DLCQ Strings, Twist Fields and One-Loop Correlators on a Permutation Orbifold

We investigate some aspects of the relationship between matrix string theory and light-cone string field theory by analysing the correspondence between the two-loop thermal partition function of DLCQ strings in flat space and the integrated two-point correlator of twist fields in a symmetric product orbifold conformal field theory at one-loop order. This is carried out by deriving combinatorial expressions for generic twist field correlation functions in permutation orbifolds using the covering surface method, by deriving the one-loop modification of the twist field interaction vertex, and by relating the two-loop finite temperature DLCQ string theory to the theory of Prym varieties for genus two covers of an elliptic curve. The case of bosonic Z(2) orbifolds is worked out explicitly and precise agreement between both amplitudes is found. We use these techniques to derive explicit expressions for Z(2) orbifold spin twist field correlation functions in the Type II and heterotic string theories.Comment: 48 pages, 1 figure; v2: typos correcte