A note on the identity module in $c=0$ CFTs
Yifei He, Hubert Saleur
SciPost Phys. 12, 100 (2022) · published 21 March 2022
- doi: 10.21468/SciPostPhys.12.3.100
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Abstract
It has long been understood that non-trivial Conformal Field Theories (CFTs) with vanishing central charge ($c=0$) are logarithmic. So far however, the structure of the identity module -- the (left and right) Virasoro descendants of the identity field -- had not been elucidated beyond the stress-energy tensor $T$ and its logarithmic partner $t$ (the solution of the "$c\to 0$ catastrophe"). In this paper, we determine this structure together with the associated OPE of primary fields up to level $h=\bar{h}=2$ for polymers and percolation CFTs. This is done by taking the $c\to 0$ limit of $O(n)$ and Potts models and combining recent results from the bootstrap with arguments based on conformal invariance and self-duality. We find that the structure contains a rank-3 Jordan cell involving the field $T\bar{T}$, and is identical for polymers and percolation. It is characterized in part by the common value of a non-chiral logarithmic coupling $a_0=-{25\over 48}$.
Cited by 3
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Yifei He,
- 1 3 Hubert Saleur
- 1 Université Paris-Saclay / University of Paris-Saclay
- 2 École Normale Supérieure [ENS]
- 3 University of Southern California [USC]