The quantum superstring as a WZNW model with N=2 superconformal symmetry

P. A. Grassi; G. Policastro; P. van Nieuwenhuizen

doi:10.1016/j.nuclphysb.2003.10.008

The quantum superstring as a WZNW model with N=2 superconformal symmetry

P. A. Grassi
, G. Policastro
, P. van Nieuwenhuizen

Research output: Contribution to journal › Article › peer-review

Abstract

We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. To incorporate worldsheet diffeomorphisms we need the quartet of ghosts (b_zz,c^z, β_zz, γ^z) for topological gravity. The currents of this combined system form an N=2 superconformal algebra. The model has vanishing central charge and contains two anticommuting BRST charges, Q_S=Q_W+∮γ ^zb_zz and Q_V=∮c^z (T^W_zz+ (1/2)T^top_zz)+γ ^z(B^W _zz+(1/2)B^top _zz-(1/2)c^z F_zzz-(1/4)γ ^zΦ_zzz). Physical states form the cohomology of Q_S+Q_V+∮η _z, where η_z is obtained by the usual fermionization of β_zz,γ^z, have non-negative grading, and are annihilated by b₀ and β₀. We no longer introduce any ghosts by hand, and the formalism is completely Lorentz covariant.

Original language	English
Pages (from-to)	43-63
Number of pages	21
Journal	Nuclear Physics B
Volume	676
Issue number	1-2
DOIs	https://doi.org/10.1016/j.nuclphysb.2003.10.008
Publication status	Published - 5 Jan 2004
Externally published	Yes

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title = "The quantum superstring as a WZNW model with N=2 superconformal symmetry",

abstract = "We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. To incorporate worldsheet diffeomorphisms we need the quartet of ghosts (bzz,cz, βzz, γz) for topological gravity. The currents of this combined system form an N=2 superconformal algebra. The model has vanishing central charge and contains two anticommuting BRST charges, QS=QW+∮γ zbzz and QV=∮cz (TWzz+ (1/2)Ttopzz)+γ z(BW zz+(1/2)Btop zz-(1/2)cz Fzzz-(1/4)γ zΦzzz). Physical states form the cohomology of QS+QV+∮η z, where ηz is obtained by the usual fermionization of βzz,γz, have non-negative grading, and are annihilated by b0 and β0. We no longer introduce any ghosts by hand, and the formalism is completely Lorentz covariant.",

author = "Grassi, \{P. A.\} and G. Policastro and \{van Nieuwenhuizen\}, P.",

note = "Funding Information: We thank the Ecole Normale Sup{\'e}rieure at Paris and its director Eug{\`e}ne Cremmer for a stay of a month during which this work was begun. Part of this research was supported by NSF Grant PHY-0098527. G.P. is supported by PPARC. ",

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doi = "10.1016/j.nuclphysb.2003.10.008",

language = "English",

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AU - Grassi, P. A.

AU - Policastro, G.

AU - van Nieuwenhuizen, P.

N1 - Funding Information: We thank the Ecole Normale Supérieure at Paris and its director Eugène Cremmer for a stay of a month during which this work was begun. Part of this research was supported by NSF Grant PHY-0098527. G.P. is supported by PPARC.

PY - 2004/1/5

Y1 - 2004/1/5

N2 - We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. To incorporate worldsheet diffeomorphisms we need the quartet of ghosts (bzz,cz, βzz, γz) for topological gravity. The currents of this combined system form an N=2 superconformal algebra. The model has vanishing central charge and contains two anticommuting BRST charges, QS=QW+∮γ zbzz and QV=∮cz (TWzz+ (1/2)Ttopzz)+γ z(BW zz+(1/2)Btop zz-(1/2)cz Fzzz-(1/4)γ zΦzzz). Physical states form the cohomology of QS+QV+∮η z, where ηz is obtained by the usual fermionization of βzz,γz, have non-negative grading, and are annihilated by b0 and β0. We no longer introduce any ghosts by hand, and the formalism is completely Lorentz covariant.

AB - We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. To incorporate worldsheet diffeomorphisms we need the quartet of ghosts (bzz,cz, βzz, γz) for topological gravity. The currents of this combined system form an N=2 superconformal algebra. The model has vanishing central charge and contains two anticommuting BRST charges, QS=QW+∮γ zbzz and QV=∮cz (TWzz+ (1/2)Ttopzz)+γ z(BW zz+(1/2)Btop zz-(1/2)cz Fzzz-(1/4)γ zΦzzz). Physical states form the cohomology of QS+QV+∮η z, where ηz is obtained by the usual fermionization of βzz,γz, have non-negative grading, and are annihilated by b0 and β0. We no longer introduce any ghosts by hand, and the formalism is completely Lorentz covariant.

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U2 - 10.1016/j.nuclphysb.2003.10.008

DO - 10.1016/j.nuclphysb.2003.10.008

M3 - Article

SN - 0550-3213

VL - 676

SP - 43

EP - 63

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1-2

ER -

The quantum superstring as a WZNW model with N=2 superconformal symmetry

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