It has recently been observed that the weakly coupled plane wave matrix model has a density of states which grows exponentially at high energy. This implies that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. In this paper, we analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator in the finite temperature plane-wave matrix model 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 order two loops.

We investigate the one-loop energy shift δE 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 the non-perturbative O(g 2 2 √ λ ′ ) contribution to δE/µ predicted in [33] is in fact an artifact of these logarithmic divergences and vanishes with them, leaving an O(g 2 2 λ ′ ) contribution. Exploiting the supersymmetry algebra, we present a form for the energy shift which appears to be manifestly convergent and free of non-perturbative terms. We use this form to argue that δE/µ receives O(g 2 2 λ ′ ) contributions at every order in intermediate state impurities.

The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a Z M -orbifold of S 5 . This is shown explicitly and examined in detail in the near plane-wave limit.A significant amount of work on the AdS/CFT correspondence [1]- [3] has been inspired the idea that the planar limit of N = 4 Yang-Mills theory and its string dual might be integrable models which would be completely solvable using a Bethe Ansätz [4]- [6]. Computation of the conformal dimensions of composite operators in N = 4 Yang-Mills theory can be mapped onto the problem of solving an SU(2, 2|4) spin chain. It is known that the spin chain simplifies considerably in the limit of infinite length where dynamics are encoded in the scattering of magnons and integrability would imply a factorized S-matrix [7]. Beginning with this limit, a strategy advocated by Staudacher [8], Beisert showed that a residual SU(2|2) 2 supersymmetry and integrability determine the N = 4 S-matrix up to a phase [9], [10]. More recent work constrains [11] and essentially computes this phase [12]-[17].

The one string-loop correction to the energies of two impurity BMN states are computed using IIB light-cone string field theory with an improved 3-string vertex that has been proposed by Dobashi and Yoneya. As in previous published computations, the string vertices are truncated to the 2-impurity channel. 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 1/2 power in the t'Hooft coupling, which is generic in string field theory, and which we have previously argued cancels, we find that the 3/2 and 5/2 powers are also miraculously absent.

No abstract