A Calculation of the plane wave string Hamiltonian from N=4 super-Yang-Mills theory

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.Comment: 38 pages, Latex; v2: Comparison with string theory changed in light of corrections to string theory results in hep-th/0206073 v3; state-operator map modified; Physical interpretation and conclusions unchange

On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres

We study the time-dependent dynamics of a collection of N collapsing/expanding D0-branes in type IIA String Theory. We show that the fuzzy-S^3 and S^5 provide time-dependent solutions to the Matrix Model of D0-branes and its DBI generalisation. Some intriguing cancellations in the calculation of the non-abelian DBI Matrix actions result in the fuzzy-S^3 and S^5 having the same dynamics at large-N. For the Matrix model, we find analytic solutions describing the time-dependent radius, in terms of Jacobi elliptic functions. Investigation of the physical properties of these configurations shows that there are no bounces for the trajectory of the collapse at large-N. We also write down a set of useful identities for fuzzy-S^3, fuzzy-S^5 and general fuzzy odd-spheres.Comment: 35 pages, latex; v2: discussion in Appendix B on the large-N limit of the associator is modified, main results of paper unchange

DLCQ String Spectrum from N=2{\cal N}=2 SYM Theory

We study non planar corrections to the spectrum of operators in the ${\mathcal N}=2$ supersymmetric Yang Mills theory which are dual to string states in the maximally supersymmetric pp-wave background with a {\em compact} light-cone direction. The existence of a positive definite discrete light-cone momentum greatly simplifies the operator mixing problem. We give some examples where the contribution of all orders in non-planar diagrams can be found analytically. On the string theory side this corresponds to finding the spectrum of a string state to all orders in string loop corrections.Comment: 35 pages, no figure

BMN operators with vector impurities, Z_2 symmetry and pp-waves

We calculate the coefficients of three-point functions of BMN operators with two vector impurities. We find that these coefficients can be obtained from those of the three-point functions of scalar BMN operators by interchanging the coefficient for the symmetric-traceless representation with the coefficient for the singlet. We conclude that the Z_2 symmetry of the pp-wave string theory is not manifest at the level of field theory three-point correlators.Comment: 25 pages, 7 figures. v1: A reference and a footnote added; v2: New contributions found, Z_2 symmetry lost in 3-point function

Simultaneous mesoscopic and two-photon imaging of neuronal activity in cortical circuits.

Spontaneous and sensory-evoked activity propagates across varying spatial scales in the mammalian cortex, but technical challenges have limited conceptual links between the function of local neuronal circuits and brain-wide network dynamics. We present a method for simultaneous cellular-resolution two-photon calcium imaging of a local microcircuit and mesoscopic widefield calcium imaging of the entire cortical mantle in awake mice. Our multi-scale approach involves a microscope with an orthogonal axis design where the mesoscopic objective is oriented above the brain and the two-photon objective is oriented horizontally, with imaging performed through a microprism. We also introduce a viral transduction method for robust and widespread gene delivery in the mouse brain. These approaches allow us to identify the behavioral state-dependent functional connectivity of pyramidal neurons and vasoactive intestinal peptide-expressing interneurons with long-range cortical networks. Our imaging system provides a powerful strategy for investigating cortical architecture across a wide range of spatial scales

Large-small dualities between periodic collapsing/expanding branes and brane funnels

We consider space and time dependent fuzzy spheres $S^{2p}$ arising in $D1-D(2p+1)$ intersections in IIB string theory and collapsing D(2p)-branes in IIA string theory. In the case of $S^2$, where the periodic space and time-dependent solutions can be described by Jacobi elliptic functions, there is a duality of the form $r$ to ${1 \over r}$ which relates the space and time dependent solutions. This duality is related to complex multiplication properties of the Jacobi elliptic functions. For $S^4$ funnels, the description of the periodic space and time dependent solutions involves the Jacobi Inversion problem on a hyper-elliptic Riemann surface of genus 3. Special symmetries of the Riemann surface allow the reduction of the problem to one involving a product of genus one surfaces. The symmetries also allow a generalisation of the $r$ to ${1 \over r}$ duality. Some of these considerations extend to the case of the fuzzy $S^6$.Comment: Latex, 50 pages, 2 figures ; v2 : a systematic typographical error corrected + minor change

Graviton-Scalar Interaction in the PP-Wave Background

We compute the graviton two scalar off-shell interaction vertex at tree level in Type IIB superstring theory on the pp-wave background using the light-cone string field theory formalism. We then show that the tree level vertex vanishes when all particles are on-shell and conservation of p_{+} and p_{-} are imposed. We reinforce our claim by calculating the same vertex starting from the corresponding SUGRA action expanded around the pp-wave background in the light-cone gauge.Comment: 26 pages, harvmac One reference added. A few comments changed in the introduction. The "cyclic perms." term removed from some equations as unnecessary and equations (2.38) and (3.19) are corrected accordingl

Chiral primary cubic interactions from pp-wave supergravity

We explicitly construct cubic interaction light-cone Hamiltonian for the chiral primary system involving the metric fields and the self-dual four-form fields in the IIB pp-wave supergravity. The background fields representing pp-waves exhibit SO(4)*SO(4)*Z_2 invariance. It turns out that the interaction Hamiltonian is precisely the same as that for the dilaton-axion system, except for the fact that the chiral primary system fields have the opposite parity to that of the dilaton-axion fields under the Z_2 transformation that exchanges two SO(4)'s.Comment: 14 pages, A few comments are adde

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