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Horizon Strings as 3d Black Hole Microstates

by Arjun Bagchi, Daniel Grumiller, M. M. Sheikh-Jabbari

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Daniel Grumiller
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-10-30
Date submitted: 2023-10-10 08:42
Submitted by: Grumiller, Daniel
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We propose that 3d black holes are an ensemble of tensionless null string states. These microstates typically have non-zero winding. We evaluate their partition function in the limit of large excitation numbers and show that their combinatorics reproduces the Bekenstein-Hawking entropy and its semiclassical logarithmic corrections.

Author comments upon resubmission

We have replied already to Referee 1. Below is our reply to the questions and requests by Referee 2.

Regarding the null string ``coupling constant $\kappa$,'' as discussed in the paper, $\kappa$ is a dimensionful free parameter of the null string theory and is not fixed by only null string theory requirements. In 3d, the Newton constant $G$ has a dimension of length, and $\kappa G^2$ is a dimensionless number, which we fix to 3/16 by the requirement of recovering the correct numerical coefficient in the Bekenstein-Hawking entropy. In higher dimension D, as we discuss in the last part of the paper, one should consider a null D-2 brane theory. (For that theory, there is also a dimensionless parameter $\kappa_D^{D-2} G_D^{D-1}$, where $G_D$ is the $D$-dimensional Newton constant.)

Regarding the request to add references, we point out that our paper appeared on the arXiv on Oct. 19th, 2022. The papers mentioned all appeared after our work, which would make such citations acausal. While it is true that our v2 (the version submitted to SciPost Physics) appeared on the arXiv on May 23rd, 2023, we did not include any references after October 2022 and did not alter the content of our paper essentially; our v2 merely attempted to optimize the presentation by including more explanations in the text and review material. We apologize for erroneously adding an acausal reference in our submission to SciPost Physics - this was a mistake that we have corrected in our v3.

List of changes

We have removed an acausal reference that was erroneously added in our submission to SciPost Physics (but that was not present in v1, v2, or v3 on the arXiv). The submitted version is identical to the arXiv version v3 and, apart from the layout, also identical to v2.

Published as SciPost Phys. 15, 210 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-10-20 (Invited Report)


The revisions has answered my requested change. Though the answer to the question on the tension of the null string is not satisfying to me, I would still like to recommend the manuscript for publication in its present form, considering the novel result in the work.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: good
  • grammar: excellent

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