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Conformal line defects at finite temperature
by Julien Barrat, Bartomeu Fiol, Enrico Marchetto, Alessio Miscioscia, Elli Pomoni
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Submission summary
| Authors (as registered SciPost users): | Julien Barrat · Enrico Marchetto · Alessio Miscioscia |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00012v1 (pdf) |
| Date submitted: | 2024-08-12 14:06 |
| Submitted by: | Miscioscia, Alessio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study conformal field theories at finite temperature in the presence of a temporal conformal line defect, wrapping the thermal circle, akin to a Polyakov loop in gauge theories. Although several symmetries of the conformal group are broken, the model can still be highly constrained from its features at zero temperature. In this work we show that the defect and bulk one and two-point correlators can be written as functions of zero-temperature data and thermal one-point functions (defect and bulk). The defect one-point functions are new data and they are induced by thermal effects of the bulk. For this new set of data we derive novel sum rules and establish a bootstrap problem for the thermal defect one-point functions from the KMS condition. We also comment on the behaviour of operators with large scaling dimensions. Additionally, we relate the free energy and entropy density to the OPE data through the one-point function of the stress-energy tensor. Our formalism is validated through analytical computations in generalized free scalar field theory, and we present new predictions for the $\mathrm O(N)$ model with a magnetic impurity in the $\veps$-expansion and the large $N$ limit.
Author indications on fulfilling journal expectations
- 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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Report
This manuscript studies conformal field theory (CFT) at finite temperature with a conformal line defect extended along the thermal circle. The authors discuss how the preserved symmetries constrain simple correlation functions and give rise to new data at finite temperature. The authors then derive an inversion formula for 1-pt functions, sum rules, and a relation between thermodynamic quantities and thermal defect CFT data, before illustrating many of these ideas in two concrete examples.
The paper makes a significant contribution to the study of defects in CFT, and is likely to become a standard reference in this subject. The work is original, novel and, to the best of my knowledge, correct. The manuscript is well-structured and well-written.
Requested changes
Before I recommend this paper for publication, I would like the authors to address a few minor comments and questions:
1-Could the authors check if their powers of z in eqs. (2.16) and (2.17) should be -\Delta-1? Also, a factor of 2\pi i from the Mellin (rather than Laplace) transform seems to have gone missing.
2-Below eq. (3.5) the authors claim that only primary operators contribute in that equation. Could the authors clarify if they mean bulk or defect primaries?
3-The presentation in section 4.2 could benefit from some further clarifications, especially the discussion around eqs. (4.18) to (4.20).
4-The vanishing of the entropy at T=0 in eq. (5.19) should be argued more carefully.
5-The second term on the RHS of eq. (5.36) should read 1/2 \sigma(\phi_i\phi_i).
6-Could the authors check the subscripts in their expression for c_0 in the paragraph following eq. (5.40), and in (5.42)? I believe \sigma -> \phi_1 there. Also, the bulk-to-defect couplings in the last paragraph of sec. 5 should be normalised by c_0 if I’m not mistaken.
7-The authors may wish to add some recent references on p.32 about defect fusion at T=0, e.g. 2102.00718, 2202.03471, 2304.10239.
8-In appendix A, could the authors comment on broken Ward identities with disorder-type defects?
Recommendation
Ask for minor revision
Report
This paper studies conformal field theories at finite temperature in the presence of a defect. The authors study one- and two-point functions. They establish sum rules and set up a bootstrap problem. The input for their approach are the T=0 in data and thermal one-point functions. They check their approach in a free field theory and make predictions for the O(n) model. The paper is very well written and new. It contains interesting material that is of interest and if important for the future study of CFTs. I recommend this paper for publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)