nLab
automorphism of a vertex operator algebra

Contents

Context

Algebra

String theory

Contents

Idea

Given a vertex operator algebra 𝒱\mathcal{V} (VOA) or super vertex operator algebra (sVOA), or more generally a full 2d CFT (of which the VOA is the local and chiral data) or 2d SCFT (hence a “2-spectral triple”) one may ask (as for any object in any category) for its automorphisms, hence the homomorphisms

𝒱𝒱 \mathcal{V} \overset{\simeq}{\longrightarrow} \mathcal{V}

in the corresponding category of sVOA-s/2d SCFTs, from 𝒱\mathcal{V} to itself, which are invertible and hence constitute a symmetry of 𝒱\mathcal{V}.

In perturbative string vacua and Connes-Lott models

If 𝒱\mathcal{V} is a direct summand of a 2d CFT/2-spectral triple encoding a perturbative string theory vacuum, such as, typically, a rational 2d CFT such as a Gepner model encoding a “non-geometricKK-compactification, then the automorphisms of 𝒱\mathcal{V} are the formal duals to symmetries of that KK-compactification-fiber space (see the references below)

In the point-particle limit where the 2d SCFT/2-spectral triple becomes an ordinary spectral triple (see there) this hence reduces to the automorphisms of internal algebras as discussed in Connes-Lott-Chamseddine-Barrett models.

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Examples

Moonshine

moonshine-examples:

References

General

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As symmetries of non-geometric string compactifications

Automorphisms of vertex operator algebras regarded as symmetries of non-geometric perturbative string theory vacua (e.g. Gepner models):

  • Chris Hull, Dan Israel, Alessandra Sarti, Non-geometric Calabi-Yau Backgrounds and K3 automorphisms, JHEP11(2017)084 (arXiv:1710.00853)

Moonshine automorphism groups

Last revised on May 20, 2019 at 04:58:02. See the history of this page for a list of all contributions to it.