Logarithmic operators in $c=0$ bulk CFTs
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...
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2025-07-01
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| Online Access: | https://scipost.org/SciPostPhys.19.1.008 |
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| author | Yifei He |
| author_facet | Yifei He |
| author_sort | Yifei He |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-db7f7810a34b4d40a7fdeaa55f43b4da |
| institution | Matheson Library |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SciPost |
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| series | SciPost Physics |
| spelling | doaj-art-db7f7810a34b4d40a7fdeaa55f43b4da2025-07-04T10:18:28ZengSciPostSciPost Physics2542-46532025-07-0119100810.21468/SciPostPhys.19.1.008Logarithmic operators in $c=0$ bulk CFTsYifei HeWe 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.https://scipost.org/SciPostPhys.19.1.008 |
| spellingShingle | Yifei He Logarithmic operators in $c=0$ bulk CFTs SciPost Physics |
| title | Logarithmic operators in $c=0$ bulk CFTs |
| title_full | Logarithmic operators in $c=0$ bulk CFTs |
| title_fullStr | Logarithmic operators in $c=0$ bulk CFTs |
| title_full_unstemmed | Logarithmic operators in $c=0$ bulk CFTs |
| title_short | Logarithmic operators in $c=0$ bulk CFTs |
| title_sort | logarithmic operators in c 0 bulk cfts |
| url | https://scipost.org/SciPostPhys.19.1.008 |
| work_keys_str_mv | AT yifeihe logarithmicoperatorsinc0bulkcfts |