N=2 Superconformal Description of Superstring in Ramond-ramond Plane Wave Backgrounds

Using the U(4) formalism developed ten years ago, the worldsheet action for the super-string in Ramond-Ramond plane wave backgrounds is expressed in a manifestly N=(2,2) superconformally invariant manner. This simplifies the construction of consistent Ramond-Ramond plane wave backgrounds and eliminates the problems associated with light-cone interaction point operators. Although the construction of worldsheet actions for the superstring in Neveu-Schwarz backgrounds is well understood using the Ramond-Neveu-Schwarz (RNS) formalism, the worldsheet action for the superstring in Ramond-Ramond (RR) backgrounds has been less studied. Because of the important role of Ramond-Ramond backgrounds in the AdS/CFT conjectures [1], these worldsheet actions might be very useful for studying aspects of these conjectures. When the background allows a light-cone gauge choice, the most straightforward method for constructing the superstring action in Ramond-Ramond backgrounds is to use the light-cone Green-Schwarz (GS) formalism [2]. This light-cone formalism is extremely useful for computing the physical spectrum in a given background, however, it is difficult to use for computing scattering amplitudes or for determining consistency conditions on superstring backgrounds. Although the light-cone RNS formalism suffers from similar problems, in the RNS case there exists an N=1 superconformally invariant description of the superstring which can replace the light-cone description (at least when RR fields are zero). Over ten years ago, an N=2 superconformally invariant description of the superstring was proposed [3][4] which reduces in light-cone gauge to the light-cone GS description. In addition to the light-cone transverse variables which are combined into bosonic world-sheet N=2 superfields, this superconformally invariant description also contains fermionic worldsheet N=2 superfields which describe the longtitudinal variables. In a flat background , the action is quadratic and contains manifest U(4) Lorentz invariance as well as twenty manifest spacetime supersymmetries. This U(4) formalism can be obtained by gauge-fixing a " doubly-supersymmetric " action [5][6][3] where κ-symmetry is replaced by worldsheet supersymmetry, and is related to the RNS formalism by a field redefinition which maps the fermionic N=2 superconformal generators to the twisted BRST current and b ghost in the RNS formalism [7]. Recently, this U(4) formalism has also been related to the pure spinor formalism [8] for the superstring via different gauge fixings [9] of the doubly-supersymmetric action. In the pure spinor formalism of the superstring [8], all SO(9, 1) super-Poincaré in-variance is manifest but the original N=2 worldsheet superconformal invariance is hidden. Although one can use the pure spinor formalism to describe any consistent background of …