Affiliation:
1. Russian Quantum Center
2. University of Paris-Saclay
Abstract
We revisit the critical two-dimensional Ashkin–Teller model, i.e. the
\mathbb{Z}_2ℤ2
orbifold of the compactified free boson CFT at
c=1c=1.
We solve the model on the plane by computing its three-point structure
constants and proving crossing symmetry of four-point correlation
functions. We do this not only for affine primary fields, but also for
Virasoro primary fields, i.e. higher twist fields and degenerate fields.
This leads us to clarify the analytic properties of Virasoro conformal
blocks and fusion kernels at c=1c=1.
We show that blocks with a degenerate channel field should be computed
by taking limits in the central charge, rather than in the conformal
dimension. In particular, Al. Zamolodchikov’s simple explicit expression
for the blocks that appear in four-twist correlation functions is only
valid in the non-degenerate case: degenerate blocks, starting with the
identity block, are more complicated generalized theta functions.
Funder
Deutsche Forschungsgemeinschaft
European Research Council
Subject
General Physics and Astronomy