SciPost Submission Page
Modular Properties of Generalised Gibbs Ensembles
by Max Downing and Faisal Karimi
Submission summary
| Authors (as registered SciPost users): | Faisal Karimi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202410_00059v1 (pdf) |
| Date submitted: | 2024-10-28 17:19 |
| Submitted by: | Karimi, Faisal |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We investigate the modular properties of Generalised Gibbs Ensembles (GGEs) in two dimensional conformal field theories. These are obtained by inserting higher spin charges in the expressions for the partition function of the theory. We investigate the particular case where KdV charges are inserted in the GGE. We first determine an asymptotic expression for the transformed GGE. This expression is an expansion in terms of the zero modes of all the quasi-primary fields in the theory, not just the KdV charges. While these charges are non-commuting they can be re-exponentiated to give an asymptotic expression for the transformed GGE in terms of another GGE. As an explicit example we focus on the Lee-Yang model. We use the Thermodynamic Bethe Ansatz in the Lee-Yang model to first replicate the asymptotic results, and then find additional energies that need to be included in the transformed GGE in order to find the exact modular transformation.
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
Current status:
Reports on this Submission
Strengths
-The paper is clearly written
-The paper addresses a timely problem
-The paper contains original and rigorous results
-The paper cites the relevant literature
-The paper points to further developments and open problems
Weaknesses
-Many of the analytical results are very specific to the model under consideration
Report
In this paper the authors address a timely and interesting problem, namely how to analytically and numerically compute the expectation values of higher conserved quantities in 2D conformal field theories (CFTs) whose partition function is characterised as a generalised Gibbs ensemble.
The authors address this problem by employing several methods, notably, the thermodynamic Bethe ansatz approach and also by interpreting the GGE partition function, as the partition function of a Gibbs ensemble in the presence of a conformal defect.
These methods are then exemplified for a the simplest non-trivial non-unitary minimal model, the Lee-Yang CFT where in particular the TBA can be solved perturbatively in the higher spin charge coupling. It is conjectured that the TBA description of the GGE is complete in the sense that it encodes information about the averages of all higher conserved charges.
As I wrote elsewhere, this paper has many strengths and the potential weakness of containing many analytical and numerical results which are highly model specific. However, the methodology is rather general and the intention to generalise and extend the results is stated in the conclusion. It is my view that the paper deserves to be published in SciPost in its present form.
Requested changes
The paper is well written and I think that it could be published in its current form. I would like to suggest two minor changes.
1) I suggest citing the paper https://arxiv.org/abs/1203.1305 since it contains an early derivation of the TBA equations for GGEs. The fact that the driving term of the TBA should be modified by including all conserved quantities had already been pointed out in https://arxiv.org/pdf/0911.3345
2) I am not 100% sure about this since there are already a lot of Appendices in this paper. However, I would suggest that perhaps parts of subsections 5.4 and 5.5 could be moved to an Appendix too (some of the longer formulae and tables) and that this would make this section more readable.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Faisal Karimi on 2025-01-09 [id 5102]
(in reply to Report 1 on 2025-01-03)We are grateful to the referee of Report 1 on 2025-1-3 for their close reading and constructive & thoughtful comments. Considering the feedback we have received; we will update our paper and hope that these changes are sufficient:
1) We will appropriately cite the two papers that were suggested to us.
2) We have decided not to move the subsections 5.4 and 5.5 into the Appendix as we feel that (a) in agreement with the referee that we already have many Appendices and (b) we wanted to make more apparent in the main text exactly how we went about justifying how the modular transformation of the GGE is encoded in the TBA. While we agree that there are formulae in these sections that are long and cumbersome, we are not necessarily convinced that this would improve readability since a reader would have to go back and forth between the appendix and the main text.