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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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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
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.
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.
Spinor moving frame, M0brane covariant BRST quantization and intrinsic complexity of the pure spinor approach, arXiv:0707.2336[hepth], Phys
 Lett. B
"... To exhibit the possible origin of the inner complexity of the Berkovits’s pure spinor approach, we consider the covariant BRST quantization of the D=11 massless superparticle (M0–brane) in its spinor moving frame or twistorlike Lorentz harmonics formulation. The presence of additional twistorlike ..."
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Cited by 10 (8 self)
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To exhibit the possible origin of the inner complexity of the Berkovits’s pure spinor approach, we consider the covariant BRST quantization of the D=11 massless superparticle (M0–brane) in its spinor moving frame or twistorlike Lorentz harmonics formulation. The presence of additional twistorlike variables (spinor harmonics) allows us to separate covariantly the first and the second class constraints. After taking into account the second class constraints by means of Dirac brackets and after further reducing the first class constraints algebra, the dynamical system is described by the cohomology of a simple BRST charge Q susy associated to the d = 1, n = 16 supersymmetry algebra. The calculation of the cohomology of this Q susy requires a regularization which implies the complexification of the bosonic ghost associated to the κ–symmetry and further leads to a complex (nonHermitian) BRST charge ˜ Q susy which is essentially the ‘pure spinor ’ BRST charge Q B by Recently a serious breakthrough in covariant description of quantum superstring theory has been reached in the framework of the Berkovits pure spinor approach [1]: a technique for loop calculations was developed [2] and the first results were given in [2, 3]. On the other hand, the pure spinor superstring was introduced asand still remains a set of prescriptions for quantum superstring
Pure spinors, free differential algebras, and the supermembrane
 Nucl. Phys. B
"... The lagrangian formalism for the supermembrane in any 11d supergravity background is constructed in the pure spinor framework. Our gaugefixed action is manifestly BRST, supersymmetric, and 3d Lorentz invariant. The relation between the Free Differential Algebras (FDA) underlying 11d supergravity an ..."
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Cited by 10 (5 self)
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The lagrangian formalism for the supermembrane in any 11d supergravity background is constructed in the pure spinor framework. Our gaugefixed action is manifestly BRST, supersymmetric, and 3d Lorentz invariant. The relation between the Free Differential Algebras (FDA) underlying 11d supergravity and the BRST symmetry of the membrane action is exploited. The ”gaugefixing ” has a natural interpretation as the variation of the Chevalley cohomology class needed for the extension of 11d superPoincaré superalgebra to Mtheory FDA. We study the solution of the pure spinor constraints in full detail. This work is supported in part by the European Union RTN contract MRTNCT2004005104 and by the The strong regime of string theory is usually denoted Mtheory. However, up to now, the underlying fundamental theory and the degrees of freedom are still unknown. Some indications coming from the lowenergy effective action, accurately described by 11dimensional supergravity, from the presence of extended objects in string theory such as the supermembrane
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
Partition Functions, Localization, and the Chiral de Rham complex
, 2007
"... We propose a localization formula for the chiral de Rham complex generalizing the wellknown localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this is to view the nonlinear βγ system as a gauge theory. For ab ..."
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Cited by 5 (1 self)
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We propose a localization formula for the chiral de Rham complex generalizing the wellknown localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this is to view the nonlinear βγ system as a gauge theory. For abelian gauge groups we are in the realm of toric geometry. Including the bc system, the formula reproduces the known results for the elliptic genus of toric varieties. We compute the partition function of several models.
The WZNW model on PSU(1,12)
, 2006
"... According to the work of Berkovits, Vafa and Witten, the nonlinear sigma model on the supergroup PSU(1,12) is the essential building block for string theory on AdS3 ×S 3 ×T 4. Models associated with a nonvanishing value of the RR flux can be obtained through a psu(1,12) invariant marginal deform ..."
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Cited by 4 (1 self)
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According to the work of Berkovits, Vafa and Witten, the nonlinear sigma model on the supergroup PSU(1,12) is the essential building block for string theory on AdS3 ×S 3 ×T 4. Models associated with a nonvanishing value of the RR flux can be obtained through a psu(1,12) invariant marginal deformation of the WZNW model on PSU(1,12). We take this as a motivation to present a manifestly psu(1,12) covariant construction of the model at the WessZumino point, corresponding to a purely NSNS background 3form flux. At this point the model possesses an enhanced ̂psu(1,12) current algebra symmetry whose representation theory, including explicit character formulas, is developed systematically in the first part of the paper. The space of vertex operators and a free fermion representation for their correlation functions is our main subject in the second part. Contrary to a widespread claim, bosonic and fermionic fields are necessarily coupled to each other. The interaction changes the supersymmetry transformations, with drastic consequences for the multiplets of localized normalizable states in the model. It is only this fact which allows us to decompose the full state space into multiplets of the global supersymmetry. We analyze these decompositions systematically as a preparation for a forthcoming study of the RR deformation.