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37
Ten–dimensional supergravity constraints from the pure spinor formalism for the superstring,” Nucl. Phys. B635
, 2002
"... It has recently been shown that the ten-dimensional 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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It has recently been shown that the ten-dimensional 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 on-shell 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 ten-dimensional 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
Pure Spinor Formalism as an N=2 Topological String
, 2005
"... Following suggestions of Nekrasov and Siegel, a non-minimal 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 spin-one 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 non-minimal 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 spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincaré covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action.
Quantization of the Type II Superstring in a Curved Six-Dimensional Background”, Nucl. Phys. B565
, 2000
"... A sigma model action with N=2 D=6 superspace variables is constructed for the Type II superstring compactified to six curved dimensions with Ramond-Ramond flux. The action can be quantized since the sigma model is linear when the six-dimensional spacetime is flat. When the six-dimensional spacetime ..."
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Cited by 36 (8 self)
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A sigma model action with N=2 D=6 superspace variables is constructed for the Type II superstring compactified to six curved dimensions with Ramond-Ramond flux. The action can be quantized since the sigma model is linear when the six-dimensional spacetime is flat. When the six-dimensional spacetime is AdS3 × S 3, the action reduces to one found earlier with Vafa and Witten. August
Supersymmetric Born-Infeld from the Pure Spinor Formalism
- of the Open Superstring”, JHEP 0301
, 2003
"... Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary ..."
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Cited by 28 (4 self)
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Classical BRST invariance in the pure spinor formalism for the open superstring is shown to imply the supersymmetric Born-Infeld equations of motion for the background fields. These equations are obtained by requiring that the left and right-moving BRST currents are equal on the worldsheet boundary in the presence of the background. The Born-Infeld equations are expressed in N=1 D=10 superspace and include all abelian contributions to the low-energy equations of motion, as well as the leading non-abelian contributions.
IFT-P.002/2002 Towards Covariant Quantization of the Supermembrane
, 2002
"... By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like inv ..."
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Cited by 26 (5 self)
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By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d=10 superparticle and superstring is extended to the d=11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λαdα where dα is the worldvolume variable corresponding to the d=11 spacetime supersymmetric derivative and λ α is an SO(10,1) pure spinor variable satisfying λΓ c λ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to Type IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving Type IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ11λ = 0, replaces the b0 L −b0R constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators.
Explaining the Pure Spinor Formalism for the Superstring
- JHEP 0801 (2008) 065, arXiv:0712.0324
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Non-Critical Pure Spinor Superstrings
, 2006
"... We construct non-critical 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 non-critical 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 non-critical pure spinor space, which is different from the ten-dimensional 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 non-critical pure spinor type IIA superstring on AdS4 with RR 4-form flux.
D-brane dynamics in constant RamondRamond potentials and noncommutative geometry,” arXiv:hep-th/0209164. 31
, 1982
"... Abstract: We study the physics of D–branes in the presence of constant Ramond–Ramond potentials. We first develop a general formalism to analyze open strings in gauge trivial closed string backgrounds, and then apply it both to the RNS string and within Berkovits ’ covariant formalism, where the res ..."
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Cited by 13 (1 self)
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Abstract: We study the physics of D–branes in the presence of constant Ramond–Ramond potentials. We first develop a general formalism to analyze open strings in gauge trivial closed string backgrounds, and then apply it both to the RNS string and within Berkovits ’ covariant formalism, where the results have the most natural interpretation. The most remarkable finding is that, in the presence of a Dp–brane, a small parallel NS–NS B–field and R–R C (p−1)–field can be gauged away to produce a U (1) field strength on the brane given by F = 1 2 B − ⋆C (p−1) ) , where ⋆ is Hodge duality along the brane world–volume. This equation differs from the usually assumed result of F = B. Note, however, that the usual result is, in the D3–brane case, not compatible with S–duality. On the other hand our result, which is derived
D–Brane Boundary States in the Pure Spinor Superstring
, 2005
"... We study the construction of D–brane boundary states in the pure spinor formalism for the quantisation of the superstring. This is achieved both via a direct analysis of the definition of D–brane boundary states in the pure spinor conformal field theory, as well as via comparison between standard RN ..."
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Cited by 6 (1 self)
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We study the construction of D–brane boundary states in the pure spinor formalism for the quantisation of the superstring. This is achieved both via a direct analysis of the definition of D–brane boundary states in the pure spinor conformal field theory, as well as via comparison between standard RNS and pure spinor descriptions of the superstring. Regarding the map between RNS and pure spinor formulations of the superstring, we shed new light on the tree level zero mode saturation rule. Within the pure spinor formalism we propose an explicit expression for the D–brane boundary state in a flat spacetime background. While the non–zero mode sector mostly follows from a simple understanding of the pure spinor conformal field theory, the zero mode sector requires a deeper analysis which is one of the main points in this work. With the construction of the boundary states at hand, we give a prescription for calculating scattering amplitudes in the presence of a D–brane. Finally, we also briefly discuss the coupling to the world–volume gauge field and show
