Witten index in supersymmetric 3d theories revisited

We have performed a direct calculation of Witten index in N = 1,2,3 supersymmetric Yang-Mills Chern-Simons 3d theories. We do it in the framework of Born-Oppenheimer (BO) approach by putting the system into a small spatial box and studying the effective Hamiltonian depending on the zero field harmonics. At the tree level, our results coincide with the results of Witten, but there is a difference in the way the loop effects are implemented. In Witten's approach, one has only take into account the fermion loops, which bring about a negative shift of the (chosen positive at the tree level) Chern-Simons coupling k. As a result, Witten index vanishes and supersymmetry is broken at small k. In the effective BO Hamiltonian framework, fermion, gluon and ghost loops contribute on an equal footing. Fermion loop contribution to the effective Hamiltonian can be evaluated exactly, and their effect amounts to the negative shift k -> k - h/2 for N =1 and k -> k - h for N = 2,3 in the tree-level formulae for the index. In our approach, with rather natural assumptions on the structure of bosonic corrections, the shift k -> k + h brought about by the gluon loops also affects the index. Since the total shift of k is positive or zero, Witten index appears to be nonzero at nonzero k, and supersymmetry is not broken. We discuss possible reasons for such disagreement.Comment: A bug in Eq.(2.20) is fixe

The H1 forward muon spectrometer

The H1 detector started taking data at the electron-proton collider HERA in the beginning of 1992. In HERA 30 GeV electrons collide with 820 GeV protons giving a strong boost of the centre-of-mass system in the direction of the proton, also called the forward region. For the detection of high momentum muons in this region a muon spectrometer has been constructed, consisting of six drift chamber planes, three either side of a toroidal magnet. A first brief description of the system and its main parameters as well as the principles for track reconstruction and T 0 determination is given

Measurement of the Decays τ−→K∗\tau^- \to K^* ντ\nu_\tau and τ−→ρ−ντ\tau^- \to \rho^- \nu_\tau

Using the ARGUS detector at DORIS II, we have determined the branching ratios for the decays τ−→K*−vτ and τ−→ρ−vτ to be (1.23 ±0.21−0.21+0.11)% and (21.5±0.4±1.9)%, respectively. These results are in agreement with theoretical expectations based on the standard model