Proving the PP-Wave/CFT2Duality

We study the duality between IIB string theory on a pp-wave background,arising as a Penrose limit of the AdS_3 times S^3 times M, where M is T^4 (orK3), and the 2D CFT which is given by the N=(4,4) orbifold (M)^N/S_N, resolvedby a blowing-up mode. After analizying the action of the supercharges on bothsides, we establish a correspondence between the states of the two theories. Inparticular and for the T^4 case, we identify both massive and masslessoscillators on the pp-wave, with certain classes of excited states in theresolved CFT carrying large R-charge n. For the former, the excited statesinvolve fractional modes of the generators of the N=4 chiral algebra acting onthe Z_n ground states. For the latter, they involve, fractional modes of theU(1)^4_L times U(1)^4_R super-current algebra acting on the Z_n ground states.By using conformal perturbation theory we compute the leading order correctionto the conformal dimensions of the first class of states, due to the presenceof the blowing up mode. We find agreement, to this order, with thecorresponding spectrum of massive oscillators on the pp-wave. We also discussthe issue of higher order corrections.Comment: 33 page