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Generalised twisted partition functions
Abstract We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D conformal field theory (CFT). A consistency
Boundary conditions in rational conformal field theories
We develop further the theory of RationalConformalFieldTheories (RCFTs) on a cylinder with specified boundaryconditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and
Boundary Conditions in Rational Conformal Field Theories
We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion
The many faces of Ocneanu cells
We define generalised chiral vertex operators covariant under the Ocneanu ``double triangle algebra'' ${\cal A}\,$ a novel quantum symmetry intrinsic to a given rational 2-d conformal field theory.
All positive energy unitary irreducible representations of extended conformal supersymmetry
We give the list of all positive energy UIR's of the conformal superalgebra su(2, 2N). They are realized as subrepresentations of elementary representations. The latter are induced from irreducible
Dynamical derivation of vacuum operator-product expansion in Euclidean conformal quantum field theory
An expansion of the type $sub 0$ = $sub 0$ $sub 0$ + $Sigma$/sub chi/l C$sup 2$(chi/subl/) $Integral$ (dp) Q/sup chi/l (x$sub 1$,x$sub 2$;-p) w/sub chi/l(p) Q/sup chi//subl/(p;x$sub 3$,... x/subn/)
From CFT to graphs
In this paper, we pursue the discussion of the connections between rational conformal field theories (CFT) and graphs. We generalise our recent work on the relations of operator product algebra (OPA)
The octagon as a determinant
Abstract The computation of a certain class of four-point functions of heavily charged BPS operators boils down to the computation of a special form factor — the octagon. In this paper, which is
Quantum groups and fusion rules multiplicities
We perform explicitly a truncation of the tensor product of two regular representations of Uq(g) for q a root of unity and show that it coincides with the fusion rules for integrable representations
Boundary conditions in charge conjugate sl(N) WZW theories
We compute the representations (``nimreps'') of the fusion algebra of affine sl(N), which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done