Comments on the scalar propagator in AdS x S and the BMN plane wave

We discuss the scalar propagator on generic AdS_{d+1} x S^{d'+1} backgrounds. For the conformally flat situations and masses corresponding to Weyl invariant actions the propagator is powerlike in the sum of the chordal distances with respect to AdS_{d+1} and S^{d'+1}. In all other cases the propagator depends on both chordal distances separately. We discuss the KK mode summation to construct the propagator in brief. For AdS_5 x S^5 we relate our propagator to the expression in the BMN plane wave limit and find a geometric interpretation of the variables occurring in the known explicit construction on the plane wave.Comment: 7 pages, Fortsch.Phys. style, Talk given at 36th International Symposium Ahrenshoop on the Theory of Elementary Particles: Recent Developments in String/M- Theory and Field Theory, Wernsdorf, Germany, 26-30 Aug 200

Coordinate representation of particle dynamics in AdS and in generic static spacetimes

We discuss the quantum dynamics of a particle in static curved spacetimes in a coordinate representation. The scheme is based on the analysis of the squared energy operator E^2, which is quadratic in momenta and contains a scalar curvature term. Our main emphasis is on AdS spaces, where this term is fixed by the isometry group. As a byproduct the isometry generators are constructed and the energy spectrum is reproduced. In the massless case the conformal symmetry is realized as well. We show the equivalence between this quantization and the covariant quantization, based on the Klein-Gordon type equation in AdS. We further demonstrate that the two quantization methods in an arbitrary (N+1)-dimensional static spacetime are equivalent to each other if the scalar curvature terms both in the operator E^2 and in the Klein-Gordon type equation have the same coefficient equal to (N-1)/(4N).Comment: 14 pages, no figures, typos correcte

Spin transition in Gd3_3N@C80_{80}, detected by low-temperature on-chip SQUID technique

We present a magnetic study of the Gd$_3$N@C$_{80}$ molecule, consisting of a Gd-trimer via a Nitrogen atom, encapsulated in a C$_{80}$ cage. This molecular system can be an efficient contrast agent for Magnetic Resonance Imaging (MRI) applications. We used a low-temperature technique able to detect small magnetic signals by placing the sample in the vicinity of an on-chip SQUID. The technique implemented at NHMFL has the particularity to operate in high magnetic fields of up to 7 T. The Gd$_3$N@C$_{80}$ shows a paramagnetic behavior and we find a spin transition of the Gd$_3$N structure at 1.2 K. We perform quantum mechanical simulations, which indicate that one of the Gd ions changes from a $^8S_{7/2}$ state ($L=0, S=7/2$) to a $^7F_{6}$ state ($L=S=3, J=6$), likely due to a charge transfer between the C$_{80}$ cage and the ion

The focus of light - linear polarization breaks the rotational symmetry of the focal spot

We experimentally demonstrate for the first time that a linearly polarized beam is focussed to an asymmetric spot when using a high-numerical aperture focussing system. This asymmetry was predicted by Richards and Wolf [Proc.R.Soc.London A, 253, 358 (1959)] and can only be measured when a polarization insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife edge type set up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focussing theory.Comment: to be published in "Journal of Modern Optics

Development of LC-13C NMR

This study involves the development of C-13 nuclear resonance as an on-line detector for liquid chromatography (LC-C-13 NMR) for the chemical characterization of aviation fuels. The initial focus of this study was the development of a high sensitivity flow C-13 NMR probe. Since C-13 NMR sensitivity is of paramount concern, considerable effort during the first year was directed at new NMR probe designs. In particular, various toroid coil designs were examined. In addition, corresponding shim coils for correcting the main magnetic field (B sub 0) homogeneity were examined. Based on these initial probe design studies, an LC-C-13 NMR probe was built and flow C-13 NMR data was obtained for a limited number of samples

On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image

We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free theory, the conformal partial wave expansion (CPWE) of the four-point function of the scalar singlet bilinear is reorganized to make it explicitly crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge fields. We are able to analytically establish the factorized form of the fusion coefficients as well as the two-point function coefficient of the HS currents. We insist in directly computing the free correlators from bulk graphs with the unconventional branch. The three-point function of the scalar bilinear turns out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be precisely related to the CPWs of the boundary dual scalar and its shadow. The flow in the IR by Legendre transforming at leading 1/N, following the pattern of double-trace deformations, and the assumption of degeneracy of the hologram lead to the CPWE of the scalar four-point function at IR. Here we confirm some previous results, obtained from more involved computations of skeleton graphs, as well as extend some of them from d=3 to generic dimension 2<d<4.Comment: 22 pages, 5 figure

Singular Liouville fields and spiky strings in \rr^{1,2} and SL(2,\rr)

The closed string dynamics in \rr^{1,2} and SL(2,\rr) is studied within the scheme of Pohlmeyer reduction. In both spaces two different classes of string surfaces are specified by the structure of the fundamental quadratic forms. The first class in \rr^{1,2} is associated with the standard lightcone gauge strings and the second class describes spiky strings and their conformal deformations on the Virasoro coadjoint orbits. These orbits correspond to singular Liouville fields with the monodromy matrixes $\pm I$. The first class in SL(2,\rr) is parameterized by the Liouville fields with vanishing chiral energy functional. Similarly to \rr^{1,2}, the second class in SL(2,\rr) describes spiky strings, related to the vacuum configurations of the SL(2,\rr)/U(1) coset model.Comment: 37 p. 6 fi

Properties of branes in curved spacetimes

A generic property of curved manifolds is the existence of focal points. We show that branes located at focal points of the geometry satisfy special properties. Examples of backgrounds to which our discussion applies are AdS_m x S^n and plane wave backgrounds. As an example, we show that a pair of AdS_2 branes located at the north and south pole of the S^5 in AdS_5 x S^5 are half supersymmetric and that they are dual to a two-monopole solution of N=4 SU(N) SYM theory. Our second example involves spacelike branes in the (Lorentzian) plane wave. We develop a modified lightcone gauge for the open string channel, analyze in detail the cylinder diagram and establish open-closed duality. When the branes are located at focal points of the geometry the amplitude acquires most of the characteristics of flat space amplitudes. In the open string channel the special properties are due to stringy modes that become massless.Comment: 41 pages; v2:typos corrected, ref adde

Spin transition in Gd3N@C-80, detected by low-temperature on-chip SQUID technique

We present a magnetic study of the Gd3N@C80 molecule, consisting of a Gd-trimer via a nitrogen atom, encapsulated in a C80 cage. This molecular system can be an efficient contrast agent for magnetic resonance imaging (MRI) applications. We used a low-temperature technique able to detect small magnetic signals by placing the sample in the vicinity of an on-chip SQUID. The technique implemented at the National High Magnetic Field Laboratory has the particularity of being able to operate in high magnetic fields of up to 7 T. The Gd3N@C80shows a paramagnetic behavior and we find a spin transition of the Gd3N structure at 1.2 K. We perform quantum mechanical simulations, which indicate that one of the Gd ions changes from a 8S7/2 state (L = 0, S = 7/2) to a 7F6 state (L = S = 3, J = 6), likely due to a charge transfer between the C80 cage and the ion