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Ten–dimensional supergravity constraints from the pure spinor formalism for the superstring,” Nucl. Phys. B635
, 2002
"... It has recently been shown that the tendimensional superstring can be quantized using the BRST operator Q = ∮ λ α dα where λ α is a pure spinor satisfying λγ m λ = 0 and dα is the fermionic supersymmetric derivative. In this paper, the pure spinor version of superstring theory is formulated in a c ..."
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Cited by 86 (15 self)
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It has recently been shown that the tendimensional superstring can be quantized using the BRST operator Q = ∮ λ α dα where λ α is a pure spinor satisfying λγ m λ = 0 and dα is the fermionic supersymmetric derivative. In this paper, the pure spinor version of superstring theory is formulated in a curved supergravity background and it is shown that nilpotency and holomorphicity of the pure spinor BRST operator imply the onshell superspace constraints of the supergravity background. This is shown to lowest order in α ′ for the heterotic and Type II superstrings, thus providing a compact pure spinor version of the tendimensional superspace constraints for N = 1, Type IIA and Type IIB supergravities. Since quantization is straightforward using the pure spinor version of the superstring, it is expected that these methods can also For many purposes, superstring theory is most conveniently expressed as an effective field theory of its massless modes consisting of supergravity theory together with corrections arising order by order in α ′. In principle these higher order corrections can be obtained by computing scattering amplitudes or by demanding consistency of the superstring sigma model in a curved
Relating the GreenSchwarz and pure spinor formalisms for the superstring
 JHEP
, 2005
"... Abstract: Although it is not known how to covariantly quantize the GreenSchwarz (GS) superstring, there exists a semilightcone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semi ..."
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Cited by 37 (3 self)
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Abstract: Although it is not known how to covariantly quantize the GreenSchwarz (GS) superstring, there exists a semilightcone gauge choice in which the GS superstring can be quantized in a conformally invariant manner. In this paper, we prove that BRST quantization of the GS superstring in semilightcone gauge is equivalent to BRST quantization using the pure spinor formalism for the superstring
Pure Spinor Formalism as an N=2 Topological String
, 2005
"... Following suggestions of Nekrasov and Siegel, a nonminimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ = 3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spinone generator, and the formalism is interpreted as a criti ..."
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Cited by 36 (7 self)
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Following suggestions of Nekrasov and Siegel, a nonminimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ = 3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spinone generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the superPoincaré covariant computation of multiloop superstring amplitudes without picturechanging operators, the construction of a cubic open superstring field theory without contactterm problems, and a new fourdimensional version of the pure spinor formalism which computes Fterms in the spacetime action.
Explaining the Pure Spinor Formalism for the Superstring
 JHEP 0801 (2008) 065, arXiv:0712.0324
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NonCritical Pure Spinor Superstrings
, 2006
"... We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spi ..."
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Cited by 15 (3 self)
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We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spinor space is an essential ingredient of the mapping. A basic feature of the map is the requirement of doubling the superspace, which we analyze in detail. We study the structure of the noncritical pure spinor space, which is different from the tendimensional one, and its quantum anomalies. We compute the pure spinor lowest lying BRST cohomology and find an agreement with the RNS spectra. The analysis is generalized to curved backgrounds and we construct as an example the noncritical pure spinor type IIA superstring on AdS4 with RR 4form flux.
BRST quantization of the pure spinor superstring
, 2007
"... We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and nonminimal formulations, and show that they are equivalent. This is achieved by first coupling the worldsheet action to topological gravity and then procee ..."
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Cited by 11 (2 self)
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We present a derivation of the scattering amplitude prescription for the pure spinor superstring from first principles, both in the minimal and nonminimal formulations, and show that they are equivalent. This is achieved by first coupling the worldsheet action to topological gravity and then proceeding to BRST quantize this system. Our analysis includes the introduction of constant ghosts and associated auxiliary fields needed to gauge fix symmetries associated with zero modes. All fields introduced in the process of quantization can be integrated out explicitly, resulting in the prescriptions for computing scattering amplitudes that have appeared previously in the literature. The zero mode insertions in the path integral follow from the integration
Note about classical dynamics of pure spinor string on AdS(5) x S(5) background, Eur. Phys
 J. C50
, 1980
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Democratic superstring field theory: Gauge fixing
 JHEP 1103 (2011) 081
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