Towards a Worldsheet Derivation of the Maldacena Conjecture

Abstract

Intriguing connections to the twistorial formulation of N = 4 Yang-Mills are also noted.

Exploring pure spinor string theory onAdS4× ℂℙ3

“…Here we show that the same way Berkovits and Vafa [12] showed the equivalence of the A-model and the pure spinor superstring for AdS 5 × S 5 , we can show the existence of such an equivalence for any superscoset admitting a Z 4 automorphism, as is the case also for the AdS 4 × CP 3 supercoset.…”

“…This phase corresponds to the Higgs phase of the theory because the gauge symmetry completely breaks. If one looks into r → 0 limit, on top of the above Higgs phase, one can have another possibility as it is explained in [24] and [12]. In this phase, the σ S R is unconstrained but the matter variables are constrained to satisfy…”

“…Similarly to the non-linear sigma model of the AdS 5 × S 5 which was studied by Berkovits and Vafa in [12], we can write a linear gauged sigma model for the non-linear sigma model for AdS 4 × CP 3 which was given in the previous section.…”

PURE SPINOR FORMALISM FOR ${\rm Osp}({\mathcal N}\vert 4)$ BACKGROUNDS

“…Notice that in this case we have for any N a complete matching between the pure spinor fields and fermionic fields. This situation is described as a gauged linear sigma model by Berkovits and Vafa in [28]. The sigma model can be constructed as a WZW model and the corresponding Kač-Moody algebra realizes the loop generalization of the algebra of the coset.…”

“…In order to compare it with the most studied case of AdS 5 × S 5 , we recall that since there are 32 manifest supersymmetries we need to have 22 pure spinor fields in order to saturate the central charge. In [7], it has been discussed the pure spinor constraints for closed type IIB superstrings (see also [28] for pure spinor constraints written in PSU(2, 2|4) basis) and it has been noticed that they are sufficient to compensate the rest of the coordinates. In the case of AdS 4 × P 3 , with less conserved supersymmetry we consistently remove 8 fermionic coordinates and 8 pure spinors from the 32 fermionic θ coordinates and from the 22 pure spinors, leading to the result of the present paper.…”