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Logarithmic operators in c=0 bulk CFTs
by Yifei He
Submission summary
| Authors (as registered SciPost users): | Yifei He |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2411.18696v1 (pdf) |
| Date submitted: | 2025-01-23 17:12 |
| Submitted by: | He, Yifei |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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→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.
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- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
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The paper deals with the c->0 limit of a few families of CFTs, and studies in great detail the logarithmic operators that one finds in this limit. Both rank-2 and higher ranks logarithmic multiplets are considered. The paper has a great deals of computations and details, that could help someone already familiar with these topics. On the other hand, the amount of detailed computations, often jumping from one CFT to another, also make it harder to understand what the main points of the paper are.
Requested changes
1. Below (2.2), diagonal is a property of the theory rather than the operator: a non-diagonal theory can still contain scalar operators. Their OPE contains opertors with non zero spin.
2. Below (2.14), it is unclear why <TT>=0 should mean the operator T being at risk of being removed, given that nothing is said about other correlation functions of T with other operators of the theory. Indeed the operator is not removed.
3. Typo in (2.39), bb instead of b
4. I cannot understand the sentence below (5.5)
5. What is exactly the definition of ˆΦ2,1 appearing in (5.48)?
6. The notation of w→0 in(5.53) is very confusing, given that we already have an operator living at z=0. I reccommend sending w→∞ with the proper rescaling (what is done in (5.50)) rather than defining w=1z and sending w→0.
Recommendation
Ask for minor revision