No abstract

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N = 4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong/weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions.In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two loop level that the anomalous dimension has a finite limit when the R charge J → ∞ keeping λ/J 2 finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.

We study the BPS spectrum of the theory on a D3-brane probe in F theory. The BPS states are realized by multi-string configurations in spacetime. Only certain configurations obeying a selection rule give rise to BPS states in the four-dimensional probe theory.Using these string configurations, we determine the spectrum of N=2 SU (2) Yang-Mills.We also explore the relation between multi-string configurations, M theory membranes and self-dual strings.3/98 *

Berenstein, Maldacena, and Nastase have proposed, as a limit of the strong form of the AdS/CFT correspondence, that string theory in a particular plane wave background is dual to a certain subset of operators in the N = 4 super-Yang-Mills theory. Even though this is a priori a strong/weak coupling duality, the matrix elements of the string theory Hamiltonian, when expressed in gauge theory variables, are analytic in the 't Hooft coupling constant. This allows one to conjecture that, like the masses of excited string states, these can be recovered using perturbation theory in Yang-Mills theory.In this paper we identify the difference between the generator of scale transformations and a particular U (1) R-symmetry generator as the operator dual to the string theory Hamiltonian for nonvanishing string coupling. We compute its matrix elements and find that they agree with the string theory prediction provided that the state-operator map is modified for nonvanishing string coupling. We construct this map explicitly and calculate the anomalous dimensions of the new operators. We identify the component arising from the modification of the state-operator map with the contribution of the string theory contact terms to the masses of string states. * On leave from the Institute of Theoretical and Experimental Physics, 117259, Bol. Cheremushkinskaya, 25, Moscow, Russia. for the masses of string states at order g s from a "unitarity computation":On the string theory side this corresponds to a 1-loop computation. Subsequent string field theory analysis performed in [8] revealed that this conjecture does not hold, and the correct matrix elements of the string Hamiltonian were computed † .The issue of recovering the interactions of the string in a plane wave background from perturbative Yang-Mills theory was discussed by various authors: n-point functions were discussed in [15], [16], [18] where some tests of the conjectured matrix elements of string Hamiltonian were proposed. Computations of n-point functions via unitarity sums was discussed in [14]. Some properties of vector operators were analyzed in [10] where an apparent mismatch with unitarity computations was pointed out. A possible solution was suggested in [11]. Deformations of the world sheet action by exactly marginal operators were discussed in [17], where 1/R AdS corrections to the masses of the string states were analyzed.In this paper we will recover the expression for the matrix elements of the string Hamiltonian from a perturbative gauge theory computation. In particular, one of the main results will be that equation (1.2) holds to second order in the string coupling constant. In gauge theory these matrix elements arise as two-point functions between appropriatelydefined (multi-trace) operators. This result seems to support the suggestion in [19] that string interactions are encoded in two-point functions of appropriately-defined multi-trace operators. An essential ingredient in our derivation are the g s corrections to the stateoperator map of [1]. These correc...

We propose some analogue of the Narain lattice for CHL string. The symmetries of this lattice are the symmetries of the perturbative spectrum. We explain in this language the known results about the possible gauge groups in compactified theory. For the fourdimensional theory, we explicitly describe the action of S-duality on the background fields.We show that the moduli spaces of the six, seven and eight-dimensional compactifications coincide with the moduli spaces of the conjectured Type IIA, M Theory and F Theory duals. We classify the rational components of the boundary of the moduli space in seven, eight and nine dimensions. * On leave from the Institute of Theoretical and Experimental Physics, Moscow, 117259, Russia.