AdS/CFT for Four-Point Amplitudes involving Gravitino Exchange

In this paper we compute the tree-level four-point scattering amplitude of two dilatini and two axion-dilaton fields in type IIB supergravity in AdS5 x S5. A special feature of this process is that there is an "exotic" channel in which there are no singleparticle poles. Another novelty is that this process involves the exchange of a bulk gravitino. The amplitude is interpreted in terms of N = 4 supersymmetric Yang-Mills theory at large 't Hooft coupling. Properties of the Operator Product Expansion are used to analyze the various contributions from single- and double-trace operators in the weak and strongly coupled regimes, and to determine the anomalous dimensions of semi-short operators. The analysis is particularly clear in the exotic channel, given the absence of BPS states.Comment: 32 pages, 1 figure. Published Version. Minor change

Propagators for p-forms in AdS_{2p+1} and correlation functions in the AdS_7/(2,0) CFT correspondence

In AdS_{2p+1} we construct propagators for p-forms whose lagrangians contain terms of the form A / d A. In particular we explore the case of forms satisfying ``self duality in odd dimensions'', and the case of forms with a topological mass term. We point out that the ``complete'' set of maximally symmetric bitensors previously used in all the other propagator papers is incomplete - there exists another bitensor which can and does appear in the formulas for the propagators in this particular case. Nevertheless, its presence does not affect the other propagators computed so far. On the AdS side of the correspondence we compute the 2 and 3 point functions involving the self-dual tensor of the maximal 7d gauged supergravity (sugra), S_{\mu\nu\rho}. Since the 7 dimensional antisymmetric self-dual tensor obeys first order field equations (S + * d S=0), to get a nonvanishing 2 point function we add a certain boundary term (to satisfy the variational principle on a manifold with boundary) to the 7d action. The 3 point functions we compute are of the type SSB and SBB, describing vertex interactions with the gauge fields B_{\mu}.Comment: 21 pages, Latex file, one reference adde

Four graviton scattering amplitude from SNR8S^N\large{{\bf R}}^{8} supersymmetric orbifold sigma model

In the IR limit the Matrix string theory is expected to be described by the $S^N\R^{8}$ supersymmetric orbifold sigma model. Recently Dijkgraaf, Verlinde and Verlinde proposed a vertex that may describe the type IIA string interaction. In this paper using this interaction vertex we derive the four graviton scattering amplitude from the orbifold model in the large $N$ limit.Comment: latex, 35 pages, misprints are corrected, the final version to appear in Nucl.Phys.

New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation

Using the result of a matrix model computation of the exact glueball superpotential, we investigate the relevant mass perturbations of the Leigh-Strassler marginal ``q'' deformation of N=4 supersymmetric gauge theory. We recall a conjecture for the elliptic superpotential that describes the theory compactified on a circle and identify this superpotential as one of the Hamiltonians of the elliptic Ruijsenaars-Schneider integrable system. In the limit that the Leigh-Strassler deformation is turned off, the integrable system reduces to the elliptic Calogero-Moser system which describes the N=1^* theory. Based on these results, we identify the Coulomb branch of the partially mass-deformed Leigh-Strassler theory as the spectral curve of the Ruijsenaars-Schneider system. We also show how the Leigh-Strassler deformation may be obtained by suitably modifying Witten's M theory brane construction of N=2 theories.Comment: 13 pages, JHEP, amstex, changed JHEP to JHEP

Electron neutrino mass scale in spectrum of Dirac equation with the 5-form flux term on the AdS(5)xS(5) background

Dimensional reduction from 10 to 5 dimensions of the IIB supergravity Dirac equation written down on the AdS(5)xS(5) (+ self-dual 5-form) background provides the unambiguous values of bulk masses of Fermions in the effective 5D Randall Sundrum theory. The use of "untwisted" and "twisted" (hep-th/0012378) boundary conditions at the UV and IR ends of the warped space-time results in two towers of spectrum of Dirac equation: the ordinary one which is linear in spectral number and the "twisted" one exponentially decreasing with growth of spectral number. Taking into account of the Fermion-5-form interaction (hep-th/9811106) gives the electron neutrino mass scale in the "twisted" spectrum of Dirac equation. Profiles in extra space of the eigenfunctions of left and right "neutrinos" drastically differ which may result in the extremely small coupling of light right neutrino with ordinary matter thus joining it to plethora of candidates for Dark Matter.Comment: 11 page

Comments on Supersymmetry Algebra and Contact Term in Matrix String Theory

Following hep-th/0309238 relating the matrix string theory to the light-cone superstring field theory, we write down two supercharges in the matrix string theory explicitly. After checking the supersymmetry algebra at the leading order, we proceed to discuss higher-order contact terms.Comment: 17 pages, no figures, v2: eq. (5.1) and related appendices corrected, v3: final version to appear in JHE

Bound States in the AdS/CFT Correspondence

We consider a massive scalar field theory in anti-de Sitter space, in both minimally and non-minimally coupled cases. We introduce a relevant double-trace perturbation at the boundary, by carefully identifying the correct source and generating functional for the corresponding conformal operator. We show that such relevant double-trace perturbation introduces changes in the coefficients in the boundary terms of the action, which in turn govern the existence of a bound state in the bulk. For instance, we show that the usual action, containing no additional boundary terms, gives rise to a bound state, which can be avoided only through the addition of a proper boundary term. Another notorious example is that of a conformally coupled scalar field, supplemented by a Gibbons-Hawking term, for which there is no associated bound state. In general, in both minimally and non-minimally coupled cases, we explicitly compute the boundary terms which give rise to a bound state, and which ones do not. In the non-minimally coupled case, and when the action is supplemented by a Gibbons-Hawking term, this also fixes allowed values of the coupling coefficient to the metric. We interpret our results as the fact that the requirement to satisfy the Breitenlohner-Freedman bound does not suffice to prevent tachyonic behavior from existing in the bulk, as it must be supplemented by additional conditions on the coefficients in the boundary terms of the action.Comment: 32 pages, Latex. v2: added comments and clarifications, minor changes. v3: corrected wrong result in the non-minimally coupled case, added reference, minor changes. v4: Added new results and discussions, parts of the paper are rewritten. Final version to be published in Phys.Rev.

Four-point correlators with higher weight superconformal primaries in the AdS/CFT Correspondence

The four-point correlation function of two 1/2 BPS primaries of conformal weight $\Delta=2$ and two 1/2-BPS primaries of conformal weight $\Delta=n$ is calculated in the large 't Hooft, large $N$ limit. These operators are dual to Kaluza-Klein supergravity fields $s_k$ with masses $m^2=-4$ and $m^2=n(n-4)$. Given that the existing formalism for evaluating sums of products of SO(6) tensors that determine the effective couplings is only suitable for primaries with small conformal dimensions, we make us of an alternative formalism based on harmonic polynomials introduced by Dolan and Osborn. We then show that the supergravity lagrangian relevant to the computation is of sigma-model type (i.e., the four-derivative couplings vanish) and that the final result for the connected amplitude splits into a free and an interacting part, as expected on general grounds.Comment: 31 pages, 4 figure

Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction

The trigonometric Ruijsenaars-Schneider model is derived by symplectic reduction of Poisson-Lie symmetric free motion on the group U(n). The commuting flows of the model are effortlessly obtained by reducing canonical free flows on the Heisenberg double of U(n). The free flows are associated with a very simple Lax matrix, which is shown to yield the Ruijsenaars-Schneider Lax matrix upon reduction.Comment: 13 pages, LaTeX, minor modifications and references added in v

A new dynamical reflection algebra and related quantum integrable systems

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, and commuting traces are derived. Explicit examples are given and quantum integrable Hamiltonians are constructed. They exhibit features similar to the Ruijsenaars-Schneider Hamiltonians.Comment: 16 pages v2: signs in the classical reflection algebra correcte