TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.1.008
TI  - Logarithmic operators in $c=0$ bulk CFTs
PY  - 2025/07/04
UR  - https://scipost.org/SciPostPhys.19.1.008
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 1
SP  - 008
A1  - He, Yifei
AB  - We study Kac operators (e.g. energy operator) in percolation and self-avoiding walk bulk CFTs with central charge $c=0$. The proper normalizations of these operators can be deduced at generic $c$ by requiring the finiteness and reality of the three-point constants in cluster and loop model CFTs. At $c=0$, Kac operators become zero-norm states and the bottom fields of logarithmic multiplets, and comparison with $c<1$ Liouville CFT suggests the potential existence of arbitrarily high rank Jordan blocks. We give a generic construction of logarithmic operators based on Kac operators and focus on the rank-2 pair of the energy operator mixing with the hull operator. By taking the $c\to 0$ limit, we compute some of their conformal data and use this to investigate the operator algebra at $c=0$. Based on cluster decomposition, we find that, contrary to previous belief, the four-point correlation function of the bulk energy operator does not vanish at $c=0$, and a crucial role is played by its coupling to the rank-3 Jordan block associated with the second energy operator. This reveals the intriguing way zero-norm operators build long-range higher-point correlations through the intricate logarithmic structures in $c=0$ bulk CFTs.
ER  -

@Article{10.21468/SciPostPhys.19.1.008,
	title={{Logarithmic operators in $c=0$ bulk CFTs}},
	author={Yifei He},
	journal={SciPost Phys.},
	volume={19},
	pages={008},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.1.008},
	url={https://scipost.org/10.21468/SciPostPhys.19.1.008},
}