Low-energy spectrum of N = 4 super-Yang-Mills on T^3: flat connections, bound states at threshold, and S-duality

We study (3+1)-dimensional N=4 supersymmetric Yang-Mills theory on a spatial three-torus. The low energy spectrum consists of a number of continua of states of arbitrarily low energies. Although the theory has no mass-gap, it appears that the dimensions and discrete abelian magnetic and electric 't Hooft fluxes of the continua are computable in a semi-classical approximation. The wave-functions of the low-energy states are supported on submanifolds of the moduli space of flat connections, at which various subgroups of the gauge group are left unbroken. The field theory degrees of freedom transverse to such a submanifold are approximated by supersymmetric matrix quantum mechanics with 16 supercharges, based on the semi-simple part of this unbroken group. Conjectures about the number of normalizable bound states at threshold in the latter theory play a crucial role in our analysis. In this way, we compute the low-energy spectra in the cases where the simply connected cover of the gauge group is given by SU(n), Spin(2n+1) or Sp(2n). We then show that the constraints of S-duality are obeyed for unique values of the number of bound states in the matrix quantum mechanics. In the cases based on Spin(2n+1) and Sp(2n), the proof involves surprisingly subtle combinatorial identities, which hint at a rich underlying structure.Comment: 28 pages. v2:reference adde

Generating and sustaining long-lived spin states in 15N,15N′-azobenzene

Long-Lived spin States (LLSs) hold a great promise for sustaining non-thermal spin order and investigating various slow processes by Nuclear Magnetic Resonance (NMR) spectroscopy. Of special interest for such application are molecules containing nearly equivalent magnetic nuclei, which possess LLSs even at high magnetic fields. In this work, we report an LLS in trans-15N,15N′-azobenzene. The singlet state of the 15N spin pair exhibits a long-lived character. We solve the challenging problem of generating and detecting this LLS and further increase the LLS population by converting the much higher magnetization of protons into the 15N singlet spin order. As far as the longevity of this spin order is concerned, various schemes have been tested for sustaining the LLS. Lifetimes of 17 minutes have been achieved at 16.4 T, a value about 250 times longer than the longitudinal relaxation time of 15N in this magnetic field. We believe that such extended relaxation times, along with the photochromic properties of azobenzene, which changes conformation upon light irradiation and can be hyperpolarized by using parahydrogen, are promising for designing new experiments with photo-switchable long-lived hyperpolarization

Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.

A criterion is given for topological stability of Abelian quantum Hall states, and of Luttinger liquids at the boundaries between such states; this suggests a selection rule on states in the quantum Hall hierarchy theory. The linear response of Luttinger liquids to electromagnetic fields is described: the Hall conductance is quantized, irrespective of whether edge modes propagate in different directions.Comment: 12 pages, LaTeX (RevTeX 3.0

Cosmic Ray Origin, Acceleration and Propagation

This paper summarizes highlights of the OG3.1, 3.2 and 3.3 sessions of the XXVIth International Cosmic Ray Conference in Salt Lake City, which were devoted to issues of origin/composition, acceleration and propagation.Comment: To appear in the Summary-Rapporteur Volume of the 26th International Cosmic Ray Conference, ed. B. L. Dingus (AIP, New York, 2000). Latex, 16 pages, no figures (Minor correction to text