771 research outputs found
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 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, -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
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