Effective field theory approach to N=4 supersymmetric Yang-Mills at finite temperature

We study the perturbation expansion of the free energy of N=4 supersymmetric SU(N) Yang-Mills at finite temperature in powers of 't Hooft's coupling g^2 N in the large N limit. Infrared divergences are controlled by constructing a hierarchy of two 3 dimensional effective field theories. This procedure is applied to the calculation of the free energy to order (g^2 N)^(3/2), but it can be extended to higher order corrections.Comment: LaTeX, 10 pages, 1 figure, uses eps

Complexified sigma model and duality

We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process we discover new type of numbers which we called `complexoids' in order to emphasize their close relation with both complex numbers and matroids. It turns out that the complexoids allow to consider the analogue of the complexified sigma-model action but with (1+1)-worldsheet metric, instead of Euclidean-worldsheet metric. Our observations can be useful for further developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio

Heisenberg-invariant Kummer surfaces

We study the geometry of Nieto's quintic threefold (Barth & Nieto, J. Alg. Geom. 3, 1994) and the Kummer and abelian surfaces that correspond to special loci.Comment: Plain TeX, 17 pages. Final version, with minor corrections, to appear in Proc. Edinburgh Math. So

Lessons Learned from the Pioneers 10/11 for a Mission to Test the Pioneer Anomaly

Analysis of the radio-metric tracking data from the Pioneer 10/11 spacecraft at distances between 20--70 astronomical units (AU) from the Sun has consistently indicated the presence of an anomalous, small, constant Doppler frequency drift. The drift is a blue-shift, uniformly changing with rate a_t = (2.92 +/- 0.44) x 10^(-18) s/s^2. It can also be interpreted as a constant acceleration of a_P = (8.74 +/- 1.33) x 10^(-8) cm/s^2 directed towards the Sun. Although it is suspected that there is a systematic origin to the effect, none has been found. As a result, the nature of this anomaly has become of growing interest. Here we discuss the details of our recent investigation focusing on the effects both external to and internal to the spacecraft, as well as those due to modeling and computational techniques. We review some of the mechanisms proposed to explain the anomaly and show their inability to account for the observed behavior of the anomaly. We also present lessons learned from this investigation for a potential deep-space experiment that will reveal the origin of the discovered anomaly and also will characterize its properties with an accuracy of at least two orders of magnitude below the anomaly's size. A number of critical requirements and design considerations for such a mission are outlined and addressed.Comment: 11 pages, invited talk given at ``35th COSPAR Scientific Assebly,'' July 18-24, 2004, Paris, Franc

Directly Measured Limit on the Interplanetary Matter Density from Pioneer 10 and 11

The Pioneer 10 and 11 spacecraft had exceptional deep-space navigational capabilities. The accuracies of their orbit reconstruction were limited, however, by a small, anomalous, Doppler frequency drift that can be interpreted as an acceleration of (8.74 +/- 1.33) x 10^{-8} cm/s^2 directed toward the Sun. We investigate the possibility that this anomaly could be due to a drag on the spacecraft from their passing through the interplanetary medium. Although this mechanism is an appealing one, the existing Pioneer radiometric data would require an unexpectedly high mass density of interplanetary dust for this mechanism to work. Further, the magnitude of the density would have to be nearly constant at distances ~ 20-70 AU. Therefore, it appears that such an explanation is very unlikely, if not ruled out. Despite this, the measured frequency drift by itself places a directly-measured, model-independent limit of \lessim 3 x 10^{-19} g/cm^3 on the mass density of interplanetary dust in the outer(~20-70 AU) solar system. Lower experimental limits can be placed if one presumes a model that varies with distance. An example is the limit \lessim 6 x 10^{-20} g/cm^3 obtained for the model with an axially-symmetric density distribution that falls off as the inverse of the distance. We emphasize that the limits obtained are experimentally-measured, in situ limits. A mission to investigate the anomaly would be able to place a better limit on the density, or perhaps even to measure it.Comment: 16 pages, 2 figures, publication versio