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Quantum information and the C-theorem in de Sitter
by Nicolás Abate, Gonzalo Torroba
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Submission summary
| Authors (as registered SciPost users): | Nicolás Abate |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2409.18186v1 (pdf) |
| Date submitted: | 2024-10-12 00:30 |
| Submitted by: | Abate, Nicolás |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Information-theoretic methods have led to significant advances in nonperturbative quantum field theory in flat space. In this work, we show that these ideas can be generalized to field theories in a fixed de Sitter space. Focusing on 1+1-dimensional field theories, we derive a boosted strong subadditivity inequality in de Sitter, and show that it implies a C-theorem for renormalization group flows. Additionally, using the relative entropy, we establish a Lorentzian bound on the entanglement and thermal entropies for a field theory inside the static patch. Finally, we discuss possible connections with recent developments using unitarity methods.
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
Report
Finding quantities that decrease monotonically along the renormalization group (RG) flow is an important problem in quantum field theory (QFT). For QFT in flat spacetime, such quantities have been identified in various dimensions, such as the central charge in 2d, the F-function in 3d, and the a-anomaly in 3d. In particular, the monotonicity of the central charge in 2d is known as the C theorem. This paper takes the important step of extending the C theorem to 1+1 dimensional de Sitter spacetime using an information-theoretic method. This is an intriguing result with potential applications in cosmology. However, I have some comments below that I believe need to be addressed before I can support the paper for publication.
Introduction:
The introduction is relatively short. It would be beneficial if the authors could briefly review and discuss the following points:
1. What tools from information theory are used, and how do they apply in flat spacetime?
2. What are the main difficulties when working with dS compared to flat spacetime?
3. What is the advantage of using the information-theoretic method in dS compared to the unitarity method?
Apart from these general remarks, there are two more specific comments:
4. It's mentioned " much less is understood about theories
without Lorentz invariance". But dS has Lorentz symmetry. Do the authors mean Poincare symmetry ?
5. The authors cited papers on c-theorem [7] and a-theorem [9]. It makes more sense to also cite works on F-theorem, e.g.
"Towards the F-Theorem: N=2 Field Theories on the Three-Sphere" and
"F-Theorem without Supersymmetry".
Section 2:
1. Equation (2.23) does not necessarily imply that "it attains its minimum negative value for "\theta_0=π/2." It only indicates that the first derivative of ΔS vanishes at this point. How do the authors rule out the possibility of a local maximum instead?
Section 3:
1.I believe equation (3.1) requires more explanation, particularly regarding the meaning of the trace. Since \rho and \sigma are density matrices in different theories, they act on different Hilbert spaces. Over which Hilbert space is the trace "\tr" taken in this case?
2. Below equation (3.11), it is mentioned that the logarithmic divergence is suppressed by a^2. It seems that the authors have exchanged the order of integration and the limit a->0. Could the authors please comment on this operation?
3. S_{\thermal} in equation (3.15) is supposed to be regularized. Could the authors specify the regularization prescription used? Is this result independent of the regularization scheme?
Recommendation
Ask for minor revision
Strengths
1 - Interesting application of quantum information methods to QFT in de Sitter spacetime
Weaknesses
1- Lack of examples.
Report
This paper studies entanglement and relative entropies in QFT in de Sitter spacetime. In particular, it proves a monotonicity theorem for a C-function - equation (5.6). In addition, equation (5.24) relates this C-function to the two-point function of the trace of the stress tensor. These are interesting results that justify publication.
Requested changes
1- after equation (2.13) it is written: "In general dimensions, it is possible to supplement the UV fixed point with appropriate counterterms in order to render ∆S(V ) finite." Why? Is there a simple argument? Can you provide references?
2- Equation (3.1) assumes that the density matrices $\sigma$ and $\rho$ act on the same Hilbert space. This is not obvious because they correspond to different QFTs.
3- In equation (3.9), why is $k$ quadratic in the couplings $\lambda_I$?
4- The log divergence in (3.11) should be treated more carefully. I suppose one should study the region of small $\theta$ before expanding at small $a$.
5- Is it possible to express $\Delta C(\theta_0)$ in terms of the stress tensor two-point function? Or this is only possible for $\theta_0=\pi/2$ like in equation (5.24)?
6- It would be instructive to compute the proposed C-function in some examples, like the theory of a massive free boson or a massive free fermion.
Recommendation
Ask for minor revision