We study the supersymmetry enhancement of ABJM theory. Starting from a N = 2 supersymmetric Chern-Simons matter theory with gauge group U(2)×U(2) which is a truncated version of the ABJM theory, we find by using the monopole operator that there is additional N = 2 supersymmetry related to the gauge group. We show this additional supersymmetry can combine with N = 6 supersymmetry of the original ABJM theory to an enhanced N = 8 SUSY with gauge group U(2)×U(2) in the case k = 1, 2. We also discuss the supersymmetry enhancement of the ABJM theory with U(N )×U(N ) gauge group and find a condition which should be satisfied by the monopole operator.

We study 'Myers effect' for a bunch of D1-branes with IIB superstrings moving in one direction along the branes. We show that the 'blown-up' configuration is the helical D1-brane, which is self-supported from collapse by the axial momentum flow. The tilting angle of the helix is determined by the number of D1-branes. The radius of the helix is stabilized to a certain value depending on the number of D1-branes and the momentum carried by IIB superstrings. This is actually T-dual version of the supertube recently found as the 'blown-up' configuration of a bunch of IIA superstrings carrying D0-brane charge. It is found that the helical D1 configuration preserves one quarter of the supersymmetry of IIB vacuum.

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We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions(> 2) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein-Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb-Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight −1, which can be cast into some interesting form. We discuss some applications of the result.

We investigate cosmology of massive electrodynamics and explore the possibility whether massive photon could provide an explanation of the dark energy. The action is given by the scalar-vector-tensor theory of gravity which is obtained by nonminimal coupling of the massive Stueckelberg QED with gravity and its cosmological consequences are studied by paying a particular attention to the role of photon mass. We find that the theory allows cosmological evolution where the radiationand matter-dominated epochs are followed by a long period of virtually constant dark energy that closely mimics ΛCDM model and the main source of the current acceleration is provided by the nonvanishing photon mass governed by the relation Λ ∼ m 2 . A detailed numerical analysis shows that the nonvanishing photon mass of the order of ∼ 10 −34 eV is consistent with the current observations. This magnitude is far less than the most stringent limit on the photon mass available so far, which is of the order of m ≤ 10 −27 eV.