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A localising AdS$_3$ sigma model

by Lorenz Eberhardt, Matthias R. Gaberdiel

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Submission summary

Authors (as registered SciPost users): Lorenz Eberhardt
Submission information
Preprint Link: https://arxiv.org/abs/2505.09226v1  (pdf)
Date accepted: Aug. 4, 2025
Date submitted: June 10, 2025, 9:11 p.m.
Submitted by: Lorenz Eberhardt
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

We construct a CFT with $\mathfrak{sl}(2,\mathbb{R})_k$ symmetry at the `tensionless' point $k=3$, which is distinct from the usual $\mathrm{SL}(2,\mathbb{R})_{k=3}$ WZW model. This new CFT is much simpler than the generic WZW model: in particular its three-point functions feature momentum-conserving delta functions, and its higher-point functions localise to covering map configurations in moduli space. We establish the consistency of the theory by explicitly deriving the four-point function from the three-point data via a sum over conformal blocks. The main motivation for our construction comes from holography, and we show that various simple supersymmetric holographic dualities for $k_{\rm s}=1$ ($k=3$) can be constructed by replacing the $\mathrm{AdS}_3$ factor on the worldsheet with this alternative theory. This includes in particular the prototypical case of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$, as well as the recently discussed example of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$. However, our analysis does not require supersymmetry and also applies to bosonic ${\rm AdS}_3$ backgrounds (at $k=3$).

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

Published as SciPost Phys. 19, 060 (2025)

Reports on this Submission

Report #3 by Anonymous (Referee 3) on 2025-7-25 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2505.09226v1, delivered 2025-07-25, doi: 10.21468/SciPost.Report.11638

Report

The current manuscript provides an axiomatic definition (by specifying worldsheet correlation functions) of a "modified" sigma model with affine $\mathfrak{sl}(2,\mathbb{R})_3$ symmetry, which is related, but not equivalent, to the usual $\text{SL}(2,\mathbb{R})$ WZW model. The new model, which the authors dub $\text{SL}(2,\mathbb{R})_3'$, is defined by demanding that its correlation functions are given exactly by the localizing solutions originally found in [3]. As a strong check of the consistency of this theory, the authors explicitly show that the 4-point function admits a conformal block expansion which is crossing-symmetric, a feature which is required by the existence of an OPE expansion. Holographically, the modified worldsheet theory can be used to derive a version of the AdS/CFT correspondence, relating string theory on $\text{SL}(2,\mathbb{R})_3'\times X$ to the symmetric orbifold $\text{Sym}^N(\mathbb{R}\times X)$.

The manuscript is well-written, comprehensive, and opens many interesting avenues to future work. I recommend the article for publication as-is.

Recommendation

Publish (surpasses expectations and criteria for this Journal; among top 10%)

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

Report #2 by Anonymous (Referee 2) on 2025-6-22 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2505.09226v1, delivered 2025-06-22, doi: 10.21468/SciPost.Report.11440

Strengths

The paper addresses an interesting problem: that of what is the string theory dual of the undeformed symmetric product CFT.

Weaknesses

Perhaps due to the limited length of the manuscript, the authors do not provide a sufficiently thorough comparative analysis with previous works.

Report

In this paper, Eberhardt and Gaberdiel propose an alternative worldsheet theory for string theory on AdS(3) at critical tension k=1, which, in the bosonic case examined in detail herein, actually corresponds to k=3. The model they introduce is the so-called "prime" SL(2,R) WZW model at level k=3. This theory includes only long strings -that is, its spectrum consists exclusively of states in the principal continuous series- and features correlation functions that localize in such a way as to yield momentum-conserving amplitudes. The authors argue that the resulting model defines a consistent conformal field theory in its own right, and they analyze both its spectrum and tree-level interactions.

The central motivation for proposing this model is to address the question of what bulk theory corresponds to the undeformed symmetric orbifold CFT, particularly at the critical value k=3. The existence of such a model -one involving only long strings and a non-compact (R)eal direction in the dual CFT- has long been suggested by various dual constructions. This paper represents a significant step toward constructing an exact holographic dual of the undeformed symmetric orbifold CFT.

I found this paper very interesting.

Recommendation

Publish (surpasses expectations and criteria for this Journal; among top 10%)

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: perfect

Report #1 by Anonymous (Referee 1) on 2025-6-17 (Invited Report)

Report

This is an interesting paper and I recommend to publish it

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

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

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