TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.12.3.100
TI  - A note on the identity module in $c=0$ CFTs
PY  - 2022/03/21
UR  - https://scipost.org/SciPostPhys.12.3.100
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 12
IS  - 3
SP  - 100
A1  - He, Yifei
AU  - Saleur, Hubert
AB  - 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 $a_0=-{25\over 48}$.
ER  -

@Article{10.21468/SciPostPhys.12.3.100,
	title={{A note on the identity module in $c=0$ CFTs}},
	author={Yifei He and Hubert Saleur},
	journal={SciPost Phys.},
	volume={12},
	pages={100},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.12.3.100},
	url={https://scipost.org/10.21468/SciPostPhys.12.3.100},
}