Speaker
Maria Stella Adamo, FAU Erlangen
Abstract
We discuss the explicit construction of 2D conformal nets that extend the non-rational Heisenberg chiral conformal net, where irreducible representations (also known as DHR sectors) are all automorphisms.
To construct 2D local algebras, we introduce charged fields acting as (twisted) shifts between DHR sectors, which can be labelled by an additive subgroup Q of the real linear space of charges. When Q is the diagonal subgroup of the left and right charges, the 2D local conformal net can be obtained by including the charge shift operators. In the non-diagonal case, Q is an even lattice, and we recover locality by introducing a 2-cocycle on Q that encodes the interplay between the DHR categories of the left and right chiral components.
This talk is based on a joint project with L. Giorgetti, Y. Tanimoto, arXiv:2301.12310, arXiv:2506.01008.