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Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
by Ivano Basile, Benjamin Knorr, Alessia Platania, Marc Schiffer
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Benjamin Knorr · Alessia Platania |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2502.12290v2 (pdf) |
| Date submitted: | March 21, 2025, 4:29 p.m. |
| Submitted by: | Benjamin Knorr |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
We provide a conceptual assessment of some aspects of fundamental quantum field theories of gravity in light of foundational aspects of the swampland program. On the one hand, asymptotically safe quantum gravity may provide a simple and predictive framework, thanks to a finite number of relevant parameters. On the other hand, a (sub-)set of intertwined swampland conjectures on the consistency of quantum gravity can be argued to be universal via effective field theory considerations. We answer whether some foundational features of these frameworks are compatible. This involves revisiting and refining several arguments (and loopholes) concerning the relation between field-theoretic descriptions of gravity and general swampland ideas. We identify the thermodynamics of black holes, spacetime topology change, and holography as the core aspects of this relation. We draw lessons on the features that a field theoretic description of gravity must (not) have to be consistent with fundamental principles underlying the swampland program, and on the universality of the latter.
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
The so-called swampland program was initiated in the context of string theory. However, recently, there is growing interest in the understanding of the potential generality of such a program. In this work, the authors provide a thorough discussion on the status of the swampland conjectures in the context of asymptotically safe quantum gravity. The work is very well written, it is logically well structured and contains detailed discussions addressing foundational issues that are essential for a proper formulation of the swampland conjectures in a quantum-field theoretic formulation of quantum gravity. The manuscript also contributes to the effort of bringing together different approaches to quantum gravity. However, there are some points that the authors should clarify in a revised version to sharpen some of the arguments. I list them below.
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In the first paragraph of Sect.~3, the authors establish the class of QG theories \textit{based on QFT in spacetime}. I don't understand what this means. Even if a background-metric structure is introduced in order to make sense of QFT techniques, this is not to be thought as a QFT in spacetime in the context of QG. For instance, one can make perfect sense of a QFT by means of lattice techniques and, in the context of QG, no background structure is introduced and it makes no sense to talk about a QFT \textit{in} spacetime. It could be that the authors meant something else but in this case I suggest that an explanatory note is added.
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One of my biggest concerns lies on their argument that spacetime topology is fixed in ASQG. Formally, in a QG-bases approach, one can write the path integral as a functional integral over metrics. I do not see how such a formal construction forbids topology change to begin with. Additionally, if one writes such a path integral and use the background field method, what determines the
fixed topology'' one is performing the path integral over? If one can consistently sum over \textit{all} topologies is a different issue but I don't see how one can control the topology one is integrating over specially non-perturbatively. I emphasize that my question involves a conceptual but also a practical aspect of the ASQG program. Again, the analogy with a lattice formulation can be instructive. For instance, in a Euclidean environment, astandard QG path integral'' will sum over topologies (although, formally, the integral is over ``metrics''). In my opinion, the authors should carefully state if any additional assumption about topology change is introduced in what they call QFT-based QG. -
Regarding the content of footnote 21: Does it apply if the gravitational field emerges from a field-theoretic pre-geometric setting?
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My impression is that there is some implicit assumption in what the authors call QFT in the following sense: Members of the LQG community would say that LQG \textit{is} a QFT. Lattice approaches correspond to QFTs using a different computational scheme (compared with standard continuum techniques). Statistical models such as matrix models correspond to an alternative way of implementing the discretization in lattice approaches thus being also QFT-oriented. But in Sect. 3.4 the authors put matrix models precisely in the context of ASQG beyond QFT as if the definition of the gravitational path integral in terms of those models would correspond to a different theory. I strongly suggest that the authors establish a clear definition of what they mean by a QFT and why one should expect that a matrix (or tensor) model that would generate the same path integral of lattice QG should not agree with the continuum approach.
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One of the striking conclusions of the manuscript is that ASQG must reinterpret the meaning of BH thermodynamics. Thinking about the generalized second law and given that ``standard'' statistical/thermodynamical origin of entropy for matter degrees of freedom is valid how can BH entropy and Matter entropy be treated differently? My understanding is that in order to elucidate this, one should find a way to \textit{derive} the would-be BH entropy from the fundamental theory of ASQG. But if there is no microstate counting interpretation how one would derive it in ASQG?
After addressing the questions raised above, I envision that the paper is suitable for publication even if some of the main results need to be weakened.
Recommendation
Ask for minor revision
Strengths
2-thorough
3-extremely long list of references
Weaknesses
Report
I find the paper generally well argued, and want to especially commend the authors for their thorough review of the literature (which is much more thorough anyway than my knowledge of it). As an honest assessment of the substantial issues faced by field theoretic approaches to quantum gravity, it is a welcome addition to the efforts aimed at reconciling the various communities and potentially channeling their respective efforts on the most promising aspects. In view of this, my general tendency would be to recommend publication, provided the following two minor points are addressed.
Requested changes
First, it should be noted that the incompatibility with black hole thermodynamics has been the main objection from the string community to attempts at quantum gravity based on local field theory for almost three decades now. In particular, this objection predates and is completely independent of any landscape or swampland discussion. It would be worth emphasizing that the apparent difficulty of asymptotic safety to accommodate black hole entropy might point to a much more basic mathematical inconsistency of the theory. Relatedly, evading asymptotic darkness seems impossible without jeopardizing the validity of Einstein gravity (specifically, the formation of trapped surfaces) at long distances.
Second, I do not actually find the arguments in section 3.1 that exclude "spacetime topology change" internally entirely convincing. Again, a much more basic objection to asymptotic safety (or other local field theory approaches to quantum gravity) has been the incompatibility of local observables with diffeomorphism invariance. This is acknowledged later in the paper, where various loopholes are offered that might resolve this issue. It seems to me that if this is possible, then the same mechanism could also make these very observables "topology change invariant" much like in the context of the AdS/CFT correspondence asymptotic observables are well-defined because fluctuations of the metric and topology are confined to the interior. On a related note, I have never quite understood how the RG flow purported to lead to asymptotic safety should be compatible with diffeomorphism invariance, given that any scale or scale transformation is not. In any event, I would like to ask the authors to spell out more clearly their arguments on these points.
Recommendation
Ask for minor revision
We thank the referee for the thorough reading of our paper and their comments, to which we will reply below.
1) As the referee points out, arguments involving black-hole thermodynamics are not new. Indeed, we have specified that some of the arguments we put forth have been discussed in the extensive literature referenced in the paper, and that we revisit and improve them (discussing and addressing their loopholes) in light of a contemporary understanding. For instance, we allow asymptotically safe UV physics to be non-local. As we point out in the conclusions, if the apparent difficulty to accommodate black-hole entropy points to an inconsistency with a physical principle such as unitarity (rather than mathematical inconsistency, as the referee suggests), a non-perturbative approach such as the S-matrix bootstrap may be able to probe it. Regarding asymptotic darkness, indeed we point out that a possible loophole to the argument is the presence of infrared non-localities, whose consistency and phenomenological aspects would require a separate study.
2) In standard (possibly gravitational) QFT, diffeomorphism-invariant observables may be defined relationally, globally or asymptotically; an example is a correlator of scalar operators inserted at a given geodesic distance, which involves spacetime integrals over the insertion points. Another example is dressed or integrated operators. We added a comment on this point in Section 4.1 in the revised manuscript. The qualitative problem with making these constructions topology-change-invariant is that the very kinematics of a spacetime QFT changes (functorially) with the spacetime manifold; by contrast, holographic CFTs are local on the conformal boundary and bulk topology does not enter observables. Therefore, the issues with summing over topologies in a spacetime QFT are the main interest of Section 3. Regarding the referee's second point on RG flows, we highlighted on page 16 that indeed there are no available physical flowing scales, but the kind of functional RG commonly used in this context employs an auxiliary flowing scale, which has to be sent to zero in order to recover the quantum effective action. As we discussed on page 16, this point is related to the preceding one: if such an auxiliary flow equation could define asymptotic observables (such as scattering amplitudes) directly, without reference to any bulk topology, the resulting theory may encode spacetime topology change, although the connection to standard QFT would ostensibly become weaker. Recent work in this direction was undertaken in 2509.00156.
We hope that this answers the doubts of the referee, and that the revised manuscript can now be published in SciPost Physics.
Author: Benjamin Knorr on 2025-12-05 [id 6111]
(in reply to Report 2 on 2025-10-09)We thank the referee for the thorough reading of our paper and their comments, to which we will reply below.
1) The formal definition of a QFT requires a spacetime manifold, not necessarily a background metric. In spacetime dimensions $d\geq3$, lattice calculations rely on this difference and indeed attempt to approximate a specified manifold. In particular, a gravitational QFT requires a dynamical degree of freedom (the gravitational field) but the manifold (i.e., the global spacetime topology) has to be fixed beforehand. We comment further in the next point.
2) Our statement means that in typical QFT-based approaches to QG, no sum over spacetime topologies, for example mediated by gravitational instantons are taken into account, and hence the spacetime topology of the metric is fixed to the spacetime topology of the background metric. In brief, spacetime topology needs to be fixed to perform the path integral over geometries in QFTs. Specifically in lattice approaches, such as EDT and CDT, the spacetime topology is fixed simply by the fact that the Pachner moves that are performed during Monte Carlo simulations are by definition spacetime-topology-preserving. We added a comment (new footnote 16) on this point in the revised manuscript. More generally, the standard definitions of QFT take manifolds as input, there is no sum over manifolds (and any attempt of summing over manifolds in a path integral is problematic); formally integrating over metrics on a fixed manifold may encode a degeneration in spacetime topology at the boundary of the space of metrics, but it would not include the degrees of freedom (e.g. metrics on a different manifold, or stringy excitations) needed to describe a topological transition through this degeneration. We discussed this point on page 11.
3) Insofar as fields are concerned, the theorem applies: the gravitational field cannot be composite. If the pre-geometric object is $not$ a field, then the theorem does not apply.
4) Our definition of QFT (either functorial or algebraic) takes $manifolds$ (i.e., topological structure) as inputs, as emphasized in footnotes 13 and 22. This explicitly includes continuum and lattice formulations, and is precisely what we mean by using the formulation “QFT on spacetime”. Some matrix models such as BFSS and IKKT, which we reference on page 16, and similar approaches do not necessarily rely on having a spacetime manifold in the first place -- they live on abstract manifolds (usually in dimensions zero or one), and the usual spacetime physics would have to emerge; for example, in the case of BFSS, this is conjectured to be the spacetime physics of eleven-dimensional M-theory. Other matrix or tensor models can be thought of as discretizations of spacetime physics, dual to dynamical triangulations, and thus would still fall into the QFT category. Either way, the emergence of spacetime is, in our opinion, non-trivial, and has to be shown by advocates of such models. We expanded the sentence on page 16 where these models are mentioned, towards the end of Sect. 3.4.
5) The referee is raising exactly the question that we have left open for ASQG to research. We do not think that there is an easy or obvious answer, but to restate our point, it is either impossible to obtain BH thermodynamics in ASQG, or some other (as of yet unknown) mechanism has to be found.
We hope that this answers the doubts of the referee, and that the revised manuscript can now be published in SciPost Physics.