SciPost Submission Page
Hyperbolic string tadpole
by Atakan Hilmi Firat
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Atakan Hilmi Firat |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202308_00003v1 (pdf) |
| Date accepted: | 2023-11-27 |
| Date submitted: | 2023-08-02 15:43 |
| Submitted by: | Firat, Atakan Hilmi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Hyperbolic geometry on the one-bordered torus is numerically uniformized using Liouville theory. This geometry is relevant for the hyperbolic string tadpole vertex describing the one-loop quantum corrections of closed string field theory. We argue that the Lam\'e equation, upon fixing its accessory parameter via Polyakov conjecture, provides the input for the characterization. The explicit expressions for the Weil-Petersson metric as well as the local coordinates and the associated vertex region for the tadpole vertex are given in terms of classical torus conformal blocks. The relevance of this vertex for vacuum shift computations in string theory is highlighted.
Published as SciPost Phys. 15, 237 (2023)
Reports on this Submission
Report #2 by Matthew Headrick (Referee 2) on 2023-11-15 (Invited Report)
- Cite as: Matthew Headrick, Report on arXiv:scipost_202308_00003v1, delivered 2023-11-15, doi: 10.21468/SciPost.Report.8123
Strengths
1. Makes important progress in closed string field theory.
2. Combines different methods in a novel way.
Weaknesses
N/A
Report
The once obscure subject of closed string string field theory has enjoyed a bit of a renaissance recently due to a few key advances. The paper under review builds on one of those, the proposal by Costello-Zwiebach to use hyperbolic metrics to define the string vertices. Specifically, this paper considers the simplest non-trivial quantum vertex, the once-punctured torus. Using tools from Liouville theory, combined with numerical work, the author uniformizes the metric and finds the local coordinates around the puncture and the Weil-Petterson metric on the moduli space.
This is an essentially technical advance, and the paper is written in a technical way, but it is an advance nonetheless. This work sets the stage for more complicated vertices, such as the twice-punctured torus, that have physical implications (e.g. mass renormalization). The paper is overall well organized and well written (aside from perhaps benefitting from a quick grammar check by a native speaker). I support its publication in SciPost.
Requested changes
Optionally, the paper could benefit from a quick grammar check.
Strengths
The paper is technically stong, involving nontrivial mathematics and provides explicit results.
Weaknesses
n.a.
Report
In this paper the author determines explicit data concerning the geometry of the hyperbolic tadpole vertex using the Polyakov conjecture to relate to classical Virasoro conformal blocks on the torus. The results are for the most part an application of ideas outlined in an earlier paper (2302.12843) giving a remarkable connection between hyperbolic vertices in closed SFT and Liouville theory.
There has been a fair amount of work on the off-shell closed string tadpole amplitude in the past. The discussion of 1704.01210 assumes the $SL(2,\mathbb{C})$ cubic vertex and is able to give a quite explicit description of the Feynman region of moduli space, but gives no natural definition of the tadpole vertex. The work of 1806.00450 determines the metric of minimal area on the 1-punctured torus at a special point in moduli space inside the tadpole vertex, but results are fully numerical and a complete characterization of the tadpole vertex is not given.
In this context the power of these techniques is truly impressive. The referee recommends the paper for publication.
Requested changes
n.a.