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Hidden exceptional symmetry in the pure spinor superstring
The pure spinor formulation of superstring theory includes an interacting sector of central charge cλ=22, which can be realized as a curved βγ system on the cone over the orthogonal Grassmannian OG+(5,10). We find that the spectrum of the βγ system organizes into representations of the g=e6 affine a...
Autores principales: | , , |
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Lenguaje: | eng |
Publicado: |
2019
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Acceso en línea: | https://dx.doi.org/10.1103/PhysRevD.101.026006 http://cds.cern.ch/record/2800101 |
_version_ | 1780972609915060224 |
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author | Eager, Richard Lockhart, Guglielmo Sharpe, Eric |
author_facet | Eager, Richard Lockhart, Guglielmo Sharpe, Eric |
author_sort | Eager, Richard |
collection | CERN |
description | The pure spinor formulation of superstring theory includes an interacting sector of central charge cλ=22, which can be realized as a curved βγ system on the cone over the orthogonal Grassmannian OG+(5,10). We find that the spectrum of the βγ system organizes into representations of the g=e6 affine algebra at level -3, whose so(10)-3⊕u(1)-4 subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine e6 characters. We interpret this as an instance of a more general pattern of enhancements in curved βγ systems, which also includes the cases g=so(8) and e7, corresponding to target spaces that are cones over the complex Grassmannian Gr(2,4) and the complex Cayley plane OP2. We identify these curved βγ systems with the chiral algebras of certain two-dimensional (2D) (0,2) conformal field theories arising from twisted compactification of 4D N=2 superconformal field theories on S2. |
id | cern-2800101 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2019 |
record_format | invenio |
spelling | cern-28001012023-10-04T06:32:59Zdoi:10.1103/PhysRevD.101.026006http://cds.cern.ch/record/2800101engEager, RichardLockhart, GuglielmoSharpe, EricHidden exceptional symmetry in the pure spinor superstringhep-thParticle Physics - TheoryThe pure spinor formulation of superstring theory includes an interacting sector of central charge cλ=22, which can be realized as a curved βγ system on the cone over the orthogonal Grassmannian OG+(5,10). We find that the spectrum of the βγ system organizes into representations of the g=e6 affine algebra at level -3, whose so(10)-3⊕u(1)-4 subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine e6 characters. We interpret this as an instance of a more general pattern of enhancements in curved βγ systems, which also includes the cases g=so(8) and e7, corresponding to target spaces that are cones over the complex Grassmannian Gr(2,4) and the complex Cayley plane OP2. We identify these curved βγ systems with the chiral algebras of certain two-dimensional (2D) (0,2) conformal field theories arising from twisted compactification of 4D N=2 superconformal field theories on S2.The pure spinor formulation of superstring theory includes an interacting sector of central charge $c_{\lambda}=22$, which can be realized as a curved $\beta\gamma$ system on the cone over the orthogonal Grassmannian $\text{OG}^{+}(5,10)$. We find that the spectrum of the $\beta\gamma$ system organizes into representations of the $\mathfrak{g}=\mathfrak{e}_6$ affine algebra at level $-3$, whose $\mathfrak{so}(10)_{-3}\oplus {\mathfrak u}(1)_{-4}$ subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine $\mathfrak{e}_6$ characters. We interpret this as an instance of a more general pattern of enhancements in curved $\beta\gamma$ systems, which also includes the cases $\mathfrak{g}=\mathfrak{so}(8)$ and $\mathfrak{e}_7$, corresponding to target spaces that are cones over the complex Grassmannian $\text{Gr}(2,4)$ and the complex Cayley plane $\mathbb{OP}^2$. We identify these curved $\beta\gamma$ systems with the chiral algebras of certain $2d$ $(0,2)$ CFTs arising from twisted compactification of 4d $\mathcal{N}=2$ SCFTs on $S^2$.arXiv:1902.09504oai:cds.cern.ch:28001012019-02-25 |
spellingShingle | hep-th Particle Physics - Theory Eager, Richard Lockhart, Guglielmo Sharpe, Eric Hidden exceptional symmetry in the pure spinor superstring |
title | Hidden exceptional symmetry in the pure spinor superstring |
title_full | Hidden exceptional symmetry in the pure spinor superstring |
title_fullStr | Hidden exceptional symmetry in the pure spinor superstring |
title_full_unstemmed | Hidden exceptional symmetry in the pure spinor superstring |
title_short | Hidden exceptional symmetry in the pure spinor superstring |
title_sort | hidden exceptional symmetry in the pure spinor superstring |
topic | hep-th Particle Physics - Theory |
url | https://dx.doi.org/10.1103/PhysRevD.101.026006 http://cds.cern.ch/record/2800101 |
work_keys_str_mv | AT eagerrichard hiddenexceptionalsymmetryinthepurespinorsuperstring AT lockhartguglielmo hiddenexceptionalsymmetryinthepurespinorsuperstring AT sharpeeric hiddenexceptionalsymmetryinthepurespinorsuperstring |