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The AdS/CFT correspondence : classical, quantum, and thermodynamical aspects Young, Donovan

Abstract

Certain aspects of the AdS/CFT correspondence are studied in detail. We investigate the one-loop mass shift to certain two-impurity string states in light-cone string field theory on a plane wave background. We find that there exist logarithmic divergences in the sums over intermediate mode numbers which cancel between the cubic Hamiltonian and quartic "contact term". Analyzing the impurity non-conserving channel we find that leading, non-perturbative terms predicted in the literature are in fact an artifact of these logarithmic divergences and vanish with them. We also argue that generically, every order in intermediate state impurities contributes to the mass shift at leading perturbative order. The same mass shift is also computed using an improved 3-string vertex proposed by Dobashi and Yoneya. The result is compared with the prediction from non-planar corrections in the BMN limit of N = 4 supersymmetric Yang-Mills theory. It is found to agree at leading order--one-loop in Yang-Mills theory--and is close but not quite in agreement at order two Yang-Mills loops. Furthermore, in addition to the leading non-perturbative power in the 't Hooft coupling, we find that two higher half-integer powers are also miraculously absent. We extend the analysis to include discrete light-cone quantization, considering states with up to three units of p⁺. We study the weakly coupled plane-wave matrix model at finite temperature. This theory has a density of states which grows exponentially at high energy, implying that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. We analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator to three loop order. We show that the phase transition is indeed of first order. We also compute the correction to the Hagedorn temperature to two loop order. Finally, correlation functions of 1/4 BPS Wilson loops with the infinite family of 1/2 BPS chiral primary operators are computed in N = 4 super Yang-Mills theory by summing planar ladder diagrams. Leading loop corrections to the sum are shown to vanish. The correlation functions are also computed in the strong-coupling limit by examining the supergravity dual of the loop-loop correlator. The strong coupling result is found to agree with the extrapolation of the planar ladders. The result is related to known correlators of 1/2 BPS Wilson loops and 1/2 BPS chiral primaries by a simple re-scaling of the coupling constant, similar to an observation made in the literature, for the case of the 1/4 BPS loop vacuum expectation value.

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