Non-linear Realisation of the N=2, D=6 Supergravity

We have applied the method of dualisation to construct the coset realisation of the bosonic sector of the N=2, D=6 supergravity which is coupled to a tensor multiplet. The bosonic field equations are regained through the Cartan-Maurer equation which the Cartan form satisfies. The first-order formulation of the theory is also obtained as a twisted self-duality condition within the non-linear coset construction.Comment: 11 page

Bound States in n Dimensions (Especially n = 1 and n = 2)

We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the "right" coupling constant behaviour for large coupling.Comment: Talk given by A. Martin at Les Houches, October 2001, to appear in "Few-Body Problems

Lepton flavor violating Higgs boson decays in seesaw models: new discussions

The lepton flavor violating decay of the Standard Model-like Higgs boson (LFVHD), h->\mu\tau, is discussed in seesaw models at the one-loop level. Based on particular analytic expressions of Passarino-Veltman functions, the two unitary and 't Hooft Feynman gauges are used to compute the branching ratio of LFVHD and compare with results reported recently. In the minimal seesaw (MSS) model, the branching ratio was investigated in the whole valid range 10^{-9}-10^{15} GeV of new neutrino mass scale m_{n_6}. Using the Casas-Ibarra parameterization, this branching ratio enhances with large and increasing m_{n_6}. But the maximal value can reach only order of 10^{-11}. Interesting relations of LFVHD predicted by the MSS and inverse seesaw (ISS) model are discussed. The ratio between two LFVHD branching ratios predicted by the ISS and MSS is simply m^2_{n_6}\mu^{-2}_X, where \mu_X is the small neutrino mass scale in the ISS. The consistence between different calculations is shown precisely from analytical approach.Comment: 4 figures, 26 pages, some analytic formulas and statements are corrected. Main results are unchanged. New references added. Version published in NP

Low temperature vortex liquid states induced by quantum fluctuations in the quasi two dimensional organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}

We report the transport properties in the vortex liquid states induced by quantum fluctuations at low temperature in the layered organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}. A steep drop of the resistivity observed below about 1 K separates the liquid state into two regions. In the low resistance state at lower temperature, a finite resistivity with weak temperature dependence persists down to 100 mK at least. The finite resistivity in the vortex state at T ~= 0 K indicates the realization of quantum vortex liquid assisted by the strong quantum fluctuations instead of the thermal one. A possible origin for separating these liquid states is a remnant vortex melting line at the original position, which is obscured and suppressed by the quantum fluctuations. A non-linear behavior of the in-plane resistivity appears at large current density in only the low resistance state, but not in another vortex liquid state at higher temperature, where the thermal fluctuations are dominant. The transport properties in the low resistance state are well understood in the vortex slush concept with a short-range order of vortices. Thus the low resistance state below 1 K is considered to be a novel quantum vortex slush state.Comment: 7 pages, 5 figure