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...asily computed in a manifestly super-Poincaré covariant manner. The formalism generalizes to curved backgrounds [10] and was used to construct quantizable actions for the superstring in AdS5 × S 5 [9]=-=[11]-=-, AdS3 × S 3 [12] [13], and AdS2 × S 2 [14] backgrounds with R-R flux. In this paper, this alternative formalism will be used to construct a quantizable action for the superstring in the plane wave ba...

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...tions. It has been possible to verify that the cohomolgy of Q produces the correct superstring spectrum, in the light-cone gauge [2] and in a manifestly ten-dimensional superPoincare covariant manner =-=[3]-=-. The model can be also formulated to describe the coupling of the superstring in a background with RR fields, such as the AdS5×S 5 [4], where one-loop conformal invariance has been proved [5]. Let us...

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...the Metsaev-Tseytlin left-invariant currents g −1 dg where g takes values in the coset PSU(2,2|4) SO(4,1)×SO(5) [2]. In the large radius limit where rAdS → ∞, this action can be covariantly quantized =-=[3]-=-[4] and one can compute PSU(2, 2|4)-covariant correlation 1 functions as an expansion in [5]. However, to compare with computations in perrAdS turbative super-Yang-Mills, one needs to be able to quant...

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...e gauge fixing to make it tractable [4, 5, 6], which in turn leads to subtleties in computing scattering amplitudes.There also exists a covariant formulation of the worldsheet theory due to Berkovits =-=[7, 8]-=-, but it has not been developed to the stage where we can use it for– 2 – comparisons with gauge theory calculations, specially in the perturbative domain of weak ’tHooft coupling 1 . Perhaps, what t...

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...al and bosonic field strength, respectively. The analysis of the massive states proceeds in a similar way. At the first massive level the ghost number one weight one vertex operator has the expansion =-=[13]-=- U (1) = ∂λ α Aα + λ α ∂θ β Bαβ + ... . (2.22) In curved spaces the superspace field equations are derived by the requirement that λ α dα is holomorphic and nilpotent [14]. The construction of the clo...

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...en string disk diagrams precisely corresponds to that of an effective B–field, as previously described. In order to describe the most general picture, we switch to the pure spinor covariant formalism =-=[13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]-=- in section 5. The power of this formalism allows us to fully describe D–brane physics in constant RR potentials. The analysis of both sections 4 and 5 is at the level of small background fields (infi...

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...scattering amplitudes. It was also proven that the formalism describes correctly the superstring degrees of freedom, in fact the superstring spectrum was determined in the light-cone gauge [4] and in =-=[5]-=- it was constructed the first massive state in terms of a manifestly ten dimensional supercovariant language. Recently, Berkovits realized that his formalism admits a more geometrical origin by discov...

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...ism. The spectrum of the model is equivalent to the Green-Schwarz spectrum in the light-cone gauge [4] and it also allows to find the physical spectrum in a manifestly super-Poincaré covariant manner =-=[5]-=-. The pure spinor formalism is suitable to describe strings in background fields with Ramond-Ramond fields strengths turned on, as it happens on anti-de Sitter geometries. In this case, it has been ch...