SciPost Submission Page
Charged Quantum Fields in AdS$_2$
by Dionysios Anninos, Diego M. Hofman, Jorrit Kruthoff
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Dionysios Anninos · Jorrit Kruthoff |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1906.00924v1 (pdf) |
| Date submitted: | July 29, 2019, 2 a.m. |
| Submitted by: | Jorrit Kruthoff |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We consider quantum field theory near the horizon of an extreme Kerr black hole. In this limit, the dynamics is well approximated by a tower of electrically charged fields propagating in an $SL(2,\mathbb{R})$ invariant AdS$_2$ geometry endowed with a constant, symmetry preserving background electric field. At large charge the fields oscillate near the AdS$_2$ boundary and no longer admit a standard Dirichlet treatment. From the Kerr black hole perspective, this phenomenon is related to the presence of an ergosphere. We discuss a definition for the quantum field theory whereby we 'UV' complete AdS$_2$ by appending an asymptotically two dimensional Minkowski region. This allows the construction of a novel observable for the flux-carrying modes that resembles the standard flat space S-matrix. We relate various features displayed by the highly charged particles to the principal series representations of $SL(2,\mathbb{R})$. These representations are unitary and also appear for massive quantum fields in dS$_2$. Both fermionic and bosonic fields are studied. We find that the free charged massless fermion is exactly solvable for general background, providing an interesting arena for the problem at hand.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2019-9-14 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1906.00924v1, delivered 2019-09-14, doi: 10.21468/SciPost.Report.1176
Strengths
- explicit and thorough analysis of charged bosons and fermions in AdS2
- identification of SL(2,R) principal series as wave functions that allow flux leaking through the horizon.
- S-matrix observable for the states associated to principal series
Weaknesses
Report
Requested changes
- The authors mentioned in section 2.1 that the rep theory for SL(2,R) and that for its universal cover differ. In fact, for Lorentzian AdS2, the latter is more natural since the killing vectors do not generate close loops (there's no compact U(1) subgroup). The authors should explain/justify why they restrict to SL(2,R) rep theory. (The authors actually consider representations of the universal cover of SL(2,R) later in section 6.1 ...)
- The background gauge field in (3.4) is invariant under SL(2,R) only after a gauge transformation. Perhaps this is worth mentioning below (3.4).
- In (3.7) and below (3.8), the constant part of $\alpha_\mu$ is ambiguous with the authors' definition. This ambiguity should be fixed by demanding the U(1) and SL(2,R) currents to be orthogonal.
- Below (3.15), by "...for large enough values of r, the parameter λ becomes complex..." the authors probably meant " for small enough values of $r$..."
- in section 4.2, the authors' procedure of defining the "S-matrix" for principal series involve gluing a flat space region to the boundary of AdS2, which is not a smooth procedure. It would be good to comment on how this observable would depend on regularizations of the gluing.
- typo in the last paragraph before section 5.3, "... a particularly explicit treatment in encountered ..." should be "... a particularly explicit treatment encountered ..."
Report #2 by Anonymous (Referee 2) on 2019-9-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1906.00924v1, delivered 2019-09-08, doi: 10.21468/SciPost.Report.1156
Report
The paper is very well-written and provides several new insights into the Kerr/CFT correspondence and quantum field theory in general. I recommend that it can be published in its current form.
Report #1 by Anonymous (Referee 1) on 2019-9-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1906.00924v1, delivered 2019-09-08, doi: 10.21468/SciPost.Report.1155
Strengths
1- a novel UV completion of AdS2 gravity with an asymptotically flat region, which allows a definition of S-matrix for modes with complex conformal weight 2- it showed that the wave equation of a charged massless fermion on the general background is exactly solvable. 3- the quantization and the definition of vacua is discussed 4- It gives a nice review of SL(2) generators and their representations, and explicitly points out the relation between the principal series representation and the flux carrying modes.
Weaknesses
Report
To conclude, the paper provides an interesting new approach to the problem of superradiance on extremal Kerr black holes, and contains a collection of interesting observations. I would like to recommend the paper for publication after the authors consider the suggestions in the "requested changes" section.
Requested changes
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The discussion in the paper would be strengthened if there is a gravitational theory for which the general background (4.13) is a solution. This might be related to point 2 below. It would be good if the authors could comment on this.
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Regarding the backreaction, the Maxwell-dilaton-gravity in [16] seems to be relevant, as it is obtained from dimensional reduction of Einstein gravity on the background eq.(2.1). Besides, a detailed holographic dictionary for yet another Maxwell-dilaton-gravity has been worked out in arXiv 1608.07018. The three models [16], [57] and arXiv 1608.07018, mainly differ in the coupling between the dilaton and the gauge field. As a result, the phase space of these models are different. As such difference might play a role in the discussion of backreaction, it would be good if the authors can comment on these other models as well.
3-The authors defined two vacua. It would be helpful to comment on the connections to the Frolov-Thorne vacuum or the Unruh vacuum for the Kerr black holes.
4-I think the authors should properly cite previous works on superradiance of extremal Kerr black holes. For example, Reference [11], [15] and arXiv 0908.3909.
5-Solutions to classical wave equations for scalars, fermions, photons and gravitons on a finite temperature version of eq.(2.1) have been discussed previously in reference [15] and 0908.3909. It seems that the calculation in Poincare AdS2 (for example section 3.2) is equivalent to the near region calculation of the aforementioned papers, in the strictly extremal limit. It would be good to clarify the relations.
6-I think [11] should be mentioned in the discussion of "Dirac sea and the ergosphere", where connections between Fermi-sea, superradiance and the ergosphere has been discussed for 5d extremal black holes.
7-On page 30, it is mentioned that possible microscopic construction would be an SYK type-model with global U(1) symmetry. A notable model with complex fermions were discussed in reference [5] of the paper and arXiv 1612.00849. It would be helpful if the authors could comment on whether this model might be relevant to the current paper.