SciPost Submission Page
Quantum information and the C-theorem in de Sitter
by Nicolás Abate, Gonzalo Torroba
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: |
|
| 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
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