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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...

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Detalles Bibliográficos
Autores principales: Eager, Richard, Lockhart, Guglielmo, Sharpe, Eric
Lenguaje:eng
Publicado: 2019
Materias:
Acceso en línea:https://dx.doi.org/10.1103/PhysRevD.101.026006
http://cds.cern.ch/record/2800101
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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.
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language eng
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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
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AT lockhartguglielmo hiddenexceptionalsymmetryinthepurespinorsuperstring
AT sharpeeric hiddenexceptionalsymmetryinthepurespinorsuperstring