We study type IIA superstring theory on a PP-wave background with 24 supercharges. This model can exactly be solved and then quantized. The open string in this PP-wave background is also studied. We observe that the theory has supersymmetric Dp-branes for p = 2, 4, 6, 8.

By placing a collection of membranes in 11 dimensional background supergravity six form field and considering the non-linear action of multiple membranes we obtain the potential for transverse scalar fields of membranes at leading order and study some possible vacuum configurations. We find that the system has a stable vacuum in which is a formation of membranes into fuzzy three sphere.

Considering the cubic theory of gravity which has been constructed in [6], we study the existence of Lifshitz and hyper scaling violating Lifshitz solutions. We firstly extend the black hole solution of [6] and find that such extended solutions are valid for any value of dynamical exponent z.Next, we examine the existence of the AdS black hole solution with nonzero hyperscaling-violating exponent θ and general dynamical exponent z. We find that the solutions do exist only for θ = 0, 3 in 4 dimension and θ = 0, 4 in 5 dimension. In particular, when θ = 3(4) in 4(5) dimension, we have Lifshitz and Schwarzschild-AdS black hole solution solution for z = {0, 1}.

In this paper, we study the generation of a large scale magnetic field with amplitude of order µG in an inflationary model which has been introduced in hep/th 0310221. This inflationary model based on existence of a speed limit for inflaton field. Generating a mass for inflaton at scale above the φ IR , breaks the conformal triviality of the Maxwell equation and causes to originate a magnetic field during the inflation. The amplitude strongly depends on the details of reheating stage and also depends on the e-foldings parameter N. We find the amplitude of the primordial magnetic field at decoupling time in this inflationary background using late time behavior of the theory.