Talks

I will give a brief review on the subject of scattering amplitudes in N=4 super Yang-Mills focussing on their infinite dimensional symmetry structure at tree-level and the fate of these symmetries at loop-level in particular employing a Highs-Regulator for the IR divergencies.

The high-energy behavior of gauge theory amplitudes can be studied using the operator expansion in Wilson lines. I review the next-to-leading order calculations of the high-energy amplitudes in N=4 SYM and QCD.

The observed conservation of Baryon and Lepton number may arise because they are gauge symmetries. Models are discussed where Baryon and lepton number are the charges for a spontaneously broken U(1) gauge symmetries. The best of these models is: (1) free of Landau poles that are near the weak scale, (2) has no flavor changing neutral currents at tree level and (3) contains a dark matter candidate.

In the so-called unitary limit of quantum gases, the scattering length diverges and the theory becomes scale invariant with dynamical exponent z=2. This point occurs precisely at the crossover between strongly coupled BEC and BCS. These systems are currently under intense experimental study using cold atoms and Feshbach resonances to tune the scattering length. We developed a new approach to the statistical mechanics of gases in higher dimensions modeled after the thermodynamic Bethe ansatz, i.e. based on the exact 2-body S-matrix. Calculations of the critical temperature Tc/T_F = 0.1 are in good agreement with experiments and Monte-Carlo studies. We also calculated the ratio of viscosity to entropy density and obtained 4.7 times the conjectured lower bound of 1/4 pi, in good agreement with very recent experiments. We also present evidence for a strongly interacting version of BEC.