In this paper we would propose a form for the action of a non-BPS D-brane, which will be manifestly supersymmetric invariant and T-duality covariant. We also explicitly show that tachyon condensation on the world-volume of this brane leads to the Dirac-Born-Infeld action for a BPS $\mathrm{D}(p-1)$-brane.

Recently modified gravitational theories which mimic the behaviour of dark matter, the so-called “Mimetic Dark Matter”, have been proposed. We study the consistency of such theories with respect to the absence of ghost instability and propose a new tensor-vector-scalar theory of gravity, which is a generalization of the previous models of mimetic dark matter with additional desirable features. The original model proposed by Chamseddine and Mukhanov [JHEP 11 (2013) 135] is concluded to describe a regular pressureless dust, presuming that we consider only those configurations where the energy density of the mimetic dust remains positive under time evolution. For certain type of configurations the theory can become unstable. Both alternative modified theories of gravity, which are based on a vector field (tensor-vector theory) or a vector field and a scalar field (tensor-vector-scalar theory), are free of ghost instabilities.

We complete the Hamiltonian analysis of a specific model of nonlinear massive gravity that was started in 2012 [J. Kluson, J. High Energy Phys. 06 (2012) 170]. We identify the primary constraint and corresponding secondary constraint. We show that they are the second class constraints and hence they lead to the elimination of the additional scalar mode. We also find that the remaining constraints are the first class constraints with the structure that corresponds to the manifestly diffeomorphism-invariant theory. Finally, we determine the number of physical degrees of freedom and we show that it corresponds to the number of physical modes of massive gravity.

We analyze non-relativistic string in Newton-Cartan background that was found recently in arXiv:1705.03535. We find its Hamiltonian formulation and study structure of constraints. We also discuss a relation between string in Newton-Cartan Background and T-duality along null reduction.

In this paper we continue the study of the Hamiltonian formalism of the healthy extended Hořava-Lifshitz gravity. We find the constraint structure of given theory and argue that this is the theory with the second class constraints. Then we discuss physical consequence of this result. We also apply the Batalin-Tyutin formalism of the conversion of the system with the second class constraints to the system with the first class constraints to the case of the healthy extended Hořava-Lifshitz theory. As a result we find new theory of gravity with structure that is different from the standard formulation of Hořava-Lifshitz gravity or General Relativity.