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Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs

by Andrea E. V. Ferrari, Niklas Garner, Heeyeon Kim

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Submission summary

Authors (as registered SciPost users): Andrea Ferrari · Heeyeon Kim
Submission information
Preprint Link: https://arxiv.org/abs/2311.05087v3  (pdf)
Date accepted: 2024-07-23
Date submitted: 2024-06-28 03:25
Submitted by: Kim, Heeyeon
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical

Abstract

We initiate the study of boundary Vertex Operator Algebras (VOAs) of topologically twisted 3d $\mathcal{N}=4$ rank-0 SCFTs. This is a recently introduced class of $\mathcal{N}=4$ SCFTs that by definition have zero-dimensional Higgs and Coulomb branches. We briefly explain why it is reasonable to obtain rational VOAs at the boundary of their topological twists. When a rank-0 SCFT is realized as the IR fixed point of a $\mathcal{N}=2$ Lagrangian theory, we propose a technique for the explicit construction of its topological twists and boundary VOAs based on deformations of the holomorphic-topological twist of the $\mathcal{N}=2$ microscopic description. We apply this technique to the $B$ twist of a newly discovered family of 3d $\mathcal{N}=4$ rank-0 SCFTs ${\mathcal T}_r$ and argue that they admit the simple affine VOAs $L_r(\mathfrak{osp}(1|2))$ at their boundary. In the simplest case, this leads to a novel level-rank duality between $L_1(\mathfrak{osp}(1|2))$ and the minimal model $M(2,5)$. As an aside, we present a TQFT obtained by twisting a 3d $\mathcal{N}=2$ QFT that admits the $M(3,4)$ minimal model as a boundary VOA and briefly comment on the classical freeness of VOAs at the boundary of 3d TQFTs.

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List of changes

1. Elaborated on the OPEs of the various generators appearing in Section 4.1.

1) expanded on OPEs of perturbative generators in the $HT$ twist below Eq. (4.10)
2) spelled out OPEs of perturbative generators with boundary monopoles in the $HT$ twist below Eq. (4.14); added OPEs of boundary monopoles
3) provided example of how deformed OPEs can be deduced from associativity

2. Changed $n$ to $r$ in Eq. (2.6).

3.Changed $Q_{-,z}$ to $G_{-,z}$ in Eq. (3.11)

4.Changed $\delta_{n+\mathfrak{m},0}$ to $\delta_{n,0}$ in Eq. (4.12)

5. Changed rank $\to$ level for describing the theories $\mathcal{T}_r$

6. p.2, reworded sentence to simply say the operator realizes an action of the Virasoro algebra.

7. Added comment that $C_2$-cofiniteness is equivalent to $R_\mathcal{V}$ being finite-dimensional and that a vertex algebra is lisse if its singular support (as a module for itself) is 0-dimensional.

8. p.3, changed ``encoded into '' to ``identified with''

9. p.3, placed conditions 1) and 2) in an enumerate environment.

10. p.7, changed $SO(4)_R$ to Spin$(4)_R$

11. p.9, added a sentence at the end of section 3.2 about the deformation of the differential.

12. p.10, added an explicit statement of the boundary conditions $\mathcal{D}$ and $D$.

13. p. 16, removed the explicit statement of linear dependence.

14. p. 17, added a comment saying that the $T$-matrix of GKLSY is only determined up to an overall phase.

15. p.20, changed ``deformation'' to ``deform''

16. Added a footnote describing why we want a boundary condition without any higher operators.

17. Added a definition of the generic Dirichlet boundary condition $D_c$ when it firsts appears in the paragraph before Section 4.1.

Published as SciPost Phys. 17, 057 (2024)


Reports on this Submission

Report #3 by Anonymous (Referee 2) on 2024-7-10 (Invited Report)

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I thank the authors for their careful response to the suggestions in the previous reports. The edits have improved the paper and the exposition; I have no further suggestions, and am happy to recommend publication in SciPost Physics in this form.

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

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Report #2 by Dongmin Gang (Referee 1) on 2024-7-2 (Invited Report)

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The manuscript has been improved and is now suitable for publication without further modifications.

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

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Report #1 by Anonymous (Referee 3) on 2024-7-1 (Invited Report)

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The authors thoughtfully addressed the comments from my previous report on this paper. I was already in favour of publishing the first version sent to me, independently of the edits that I suggested. Now I recommend publication without any further comments.

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

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