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The AdS/CFT correspondence and string theory on the pp-wave Ramadanovic, Bojan

Abstract

Aspects of the AdS/CFT correspondence are studied in the pp.-wave/BMN limit. We use the light cone string field theory to investigate energy shifts of the one and two impurity states. In the case of two impurity states we find that logarithmic divergences, in the sums of intermediate states, actually cancel out between the Hamiltonian and a Q-dependent contact term”. We show how non-perturbative terms, that have previously plagued this theory, vanish as a consequence of this cancelation. We argue from this that every order of internal impurities contributes to the overall energy shift and attempt to give a systematic way of calculating such sums for the case of the simplest 3-string vertex (one proposed by diVecchia). We extend our analysis of the mass shift to the case of the most advanced 3-string vertex (proposed by Dobashi and Yoneya). We find agreement between our string field theory calculations and the leading order CFT result in the BMN limit. We also find strong similarities between our result and higher orders in the field theory, including, on the string side, the disappearance of the half-integer powers which generically do not exist in the field theory calculations. We also study the orbifolding of the pp-wave background which results in the discrete quantization of the light-cone momentum. We present the string field theory calculation for such a discreet momentum case. We also observe how a particular choice of the orbifold, results in the string theory corresponding to the quantization of the finite size giant magnon on the CFT side. We study this theory in detail with particular emphasis on its super algebra.

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