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Boundary vertex algebras for 3d $\mathcal{N}=4$ rank-0 SCFTs
by Andrea E. V. Ferrari, Niklas Garner, Heeyeon Kim
Submission summary
| Authors (as registered SciPost users): | Andrea Ferrari · Heeyeon Kim |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2311.05087v3 (pdf) |
| Date submitted: | 2024-06-28 03:25 |
| Submitted by: | Kim, Heeyeon |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| 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.