We prove that a haploid associative algebra in a C∗-tensor category C is equivalent to a Q-
system (a special C∗-Frobenius algebra) in C if and only if it is rigid. This allows us to prove …

On a conformal net 𝒜, one can consider collections of unital completely positive maps on
each local algebra 𝒜 (I), subject to natural compatibility, vacuum preserving and conformal …

We generalize the Carpi-Kawahigashi-Longo-Weiner correspondence between vertex
operator algebras and conformal nets to the case of vertex operator superalgebras and …

Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-
bounded unitary subalgebra containing the conformal vector of V. We give two sufficient …

We prove that all nice holomorphic vertex operator superalgebras (VOSAs) with central
charge at most 24 and with non-trivial odd part are unitary, apart from the hypothetical ones …

Conformal Quantum Field Theories (CFT) in 1 or 1+ 1 spacetime dimensions (respectively
called chiral and full CFTs) admit several" axiomatic"(mathematically rigorous and model …

This thesis deals with two different mathematical axiomatisations of chiral Conformal Field
Theory (CFT). On the one hand, there is the axiomatisation via Haag-Kastler axioms, in an …

The concepts of conformal covariance and chirality in 2 spacetime dimensions are
formulated and examined within the perturbative algebraic quantum field theory framework …