Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills

One-instanton contributions to the correlation functions of two gauge-invariant single-trace operators in N=4 SU(N) Yang-Mills theory are studied in semi-classical approximation in the BMN limit. The most straightforward examples involve operators with four bosonic impurities. The explicit form for the correlation functions, which determine the anomalous dimensions, follows after integration over the large number of bosonic and fermionic moduli. Our results demonstrate that the instanton contributions scale appropriately in the BMN limit. We find impressive agreement with the D-instanton contributions to mass matrix elements of the dual plane-wave IIB superstring theory, obtained in a previous paper. Not only does the dependence on the scaled coupling constants match, but the dependence on the mode numbers of the states is also in striking agreement.Comment: 52 pages, no figures, latex; V2: minor change

Strong Evidence In Favor OF The Existence Of S-Matrix For Strings In Plane Waves

Field theories on the plane wave background are considered. We discuss that for such field theories one can only form 1+1 dimensional freely propagating wave packets. We analyze tree level four point functions of scalar field theory as well as scalars coupled to gauge fields in detail and show that these four point functions are well-behaved so that they can be interpreted as S-matrix elements for 2 particle $\to$ 2 particle scattering amplitudes. Therefore, at least classically, field theories on the plane wave background have S-matrix formulation.Comment: Latex file, 26 pages, 4 eps figures. v3: In the end of paper there is a "Note Added" as an update of the result

On light-cone SFT contact terms in a plane wave

Testing the BMN correspondence at non-zero string coupling g_s requires a one-loop string field theory calculation. At order g_s^2, matrix elements of the light-cone string field theory Hamiltonian between single-string states receive two contributions: the iterated cubic interaction, and a contact term {Q, Q} whose presence is dictated by supersymmetry. In this paper we calculate the leading large mu p^+ alpha' contribution from both terms for the set of intermediate states with two string excitations. We find precise agreement with the basis-independent order g_2^2 results from gauge theory.Comment: 15 pages, 1 figur

Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry

We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter mu. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We derive asymptotic expansions for large mu and find unexpectedly simple results, which are valid to all orders in 1/mu. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified 't Hooft coupling lambda'. A specific example is presented.Comment: 28 pages, 2 figures, v2: reference added, new comments and appendix, typos fixed in eqs. (86) and (89

Divergence Cancellation and Loop Corrections in String Field Theory on a Plane Wave Background

We investigate the one-loop energy shift E 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, order g_2^2 sqrt(lambda') contribution to E/mu predicted in hep-th/0211220 is in fact an artifact of these logarithmic divergences and vanishes with them, leaving an order g_2^2 lambda' 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 E/mu receives order g_2^2 lambda' contributions at every order in intermediate state impurities.Comment: 27 pages; added references, acknowledgments, missing normalization in equations 2.3 - 2.8, also cleaned up notation, and added a few footnote

Superstrings and D-branes in A Plane Wave

We carefully analyze the supersymmetry algebra of closed strings and open strings in a type IIB plane wave background. We use eight component chiral spinors, SO(8) Majorana-Weyl spinors, in light-cone gauge to provide a useful basis of string field theory calculation in the plane wave. We consider the two classes of D-branes, $D_\pm$-branes, and give a worldsheet derivation of conserved supercurrents for all half BPS D-branes preserving 16 supersymmetries in the type IIB plane wave background. We exhaustively provide the supersymmetry algebra of the half BPS branes as well. We also point out that the supersymmetry algebra distinguishes the two SO(4) directions with relative sign which is consistent with the Z_2 symmetry of the string action.Comment: v4: 28 pages, Latex, Worldsheet derivation of conserved supercurrents for all half BPS D-branes newly added, improved presentation and typo

Non-perturbative contributions to the plane-wave string mass matrix

D-instanton contributions to the mass matrix of arbitrary excited string states of type IIB string theory in the maximally supersymmetric plane-wave background are calculated to leading order in the string coupling using a supersymmetric light-cone boundary state formalism. The explicit non-perturbative dependence of the mass matrix on the complex string coupling, the plane-wave mass parameter and the mode numbers of the excited states is determined.Comment: 25 pages, 1 figure. v3: corrected minor typos, added referenc

Strings in the near plane wave background and AdS/CFT

We study the AdS/CFT correspondence for string states which flow into plane wave states in the Penrose limit. Leading finite radius corrections to the string spectrum are compared with scaling dimensions of finite R-charge BMN-like operators. We find agreement between string and gauge theory results.Comment: 35 pages, 13 eps figures v2: minor corrections, references adde

Tracing the String: BMN correspondence at Finite J^2/N

Employing the string bit formalism of hep-th/0209215, we identify the basis transformation that relates BMN operators in N=4 gauge theory to string states in the dual string field theory at finite g_2=J^2/N. In this basis, the supercharge truncates at linear order in g_2, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of hep-th/0206073 for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g_2^2 contact term in the string bit Hamiltonian. The resulting leading order mass renormalization of string states agrees with the recently computed shift in conformal dimension of BMN operators in the gauge theory.Comment: 11 pages, 1 figur

An alternative formulation of light-cone string field theory on the plane wave

We construct a manifestly SO(4) x SO(4) invariant, supersymmetric extension of the closed string cubic interaction vertex and dynamical supercharges in light-cone string field theory on the plane wave space-time. We find that the effective vertex for states built out of bosonic creation oscillators coincides with the one previously constructed in the SO(8) formalism and conjecture that in general the two formulations are physically equivalent. Further evidence for this claim is obtained from the discrete Z_2-symmetry of the plane wave and by computing the mass-shift of the simplest stringy state using perturbation theory. We verify that the leading non-planar correction to the anomalous dimension of the dual gauge theory operators is correctly recovered.Comment: 28 pages; v2: minor change