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114
Multiloop superstring amplitudes from nonminimal pure spinor formalism
"... Using the nonminimal version of the pure spinor formalism, manifestly superPoincaré covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picturechanging operators. The only subtlety comes from regularizing the functional integral over the ..."
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Cited by 52 (4 self)
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Using the nonminimal version of the pure spinor formalism, manifestly superPoincaré covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picturechanging operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRSTinvariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to tendimensional Fterms, i.e. terms in the tendimensional superspace action which do not involve integration over the maximum number of θ’s.
Lectures on curved betagamma systems, pure spinors, and anomalies
"... The curved betagamma system is the chiral sector of a certain infinite radius limit of the nonlinear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism an ..."
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Cited by 52 (3 self)
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The curved betagamma system is the chiral sector of a certain infinite radius limit of the nonlinear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism anomalies which we review. We analyze the curved betagamma system on the space of pure spinors, aiming to verify the consistency of Berkovits covariant superstring quantization. We demonstrate that under certain conditions both anomalies can be cancelled for the pure spinor sigma model, in which case one reproduces the old construction of B. Feigin and E. Frenkel.
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.
Character of pure spinors
"... The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simp ..."
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Cited by 29 (2 self)
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The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D = 10 and D = 11 superparticle.
Pure Spinor Superspace Identities for Massless Fourpoint Kinematic Factors
, 2008
"... Using the pure spinor formalism we prove identities which relate the treelevel, oneloop and twoloop kinematic factors for massless fourpoint amplitudes. From these identities it follows that the complete supersymmetric one and twoloop amplitudes are immediately known once the treelevel kinemat ..."
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Cited by 24 (12 self)
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Using the pure spinor formalism we prove identities which relate the treelevel, oneloop and twoloop kinematic factors for massless fourpoint amplitudes. From these identities it follows that the complete supersymmetric one and twoloop amplitudes are immediately known once the treelevel kinematic factor is evaluated. In particular, the twoloop equivalence with the RNS formalism (up to an overall coefficient) is obtained as a corollary.
Explaining the Pure Spinor Formalism for the Superstring
 JHEP 0801 (2008) 065, arXiv:0712.0324
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The oneloop open superstring massless fivepoint amplitude with the nonminimal pure spinor formalism
, 2009
"... We compute the massless fivepoint amplitude of open superstrings using the nonminimal pure spinor formalism and obtain a simple kinematic factor in pure spinor superspace, which can be viewed as the natural extension of the kinematic factor of the massless fourpoint amplitude. It encodes bosonic a ..."
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Cited by 15 (6 self)
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We compute the massless fivepoint amplitude of open superstrings using the nonminimal pure spinor formalism and obtain a simple kinematic factor in pure spinor superspace, which can be viewed as the natural extension of the kinematic factor of the massless fourpoint amplitude. It encodes bosonic and fermionic external states in supersymmetric form and reduces to existing bosonic amplitudes when expanded in components, therefore proving their equivalence. We also show how to compute the kinematic structures involving fermionic states.
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.