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We extend the definition of the refined topological vertex C to an n-coloured refined topological vertex C_n that depends on n free bosons, and compute the 5D strip partition function made of N pairs of C_n vertices and conjugate C*_n vertices. Using geometric engineering and the AGT correspondence, the 4D limit of this strip partition function is identified with a (normalized) matrix element of a (primary state) vertex operator that intertwines two (arbitrary descendant) states in a (generically non-rational) 2D conformal field theory with Z_n parafermion primary states.
Supersymmetric theories with the same bosonic content but different fermions, aka emph{twins}, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic $mathcal{N}=3$ and $mathcal{N}=1
The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex fixed points a
We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE coefficients of
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFTs), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general a
Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the intertwiners betw