We use holographic techniques to study SU (N c ) super Yang-Mills theory coupled to N f ≪ N c flavours of fundamental matter at finite temperature and baryon density. We focus on four dimensions, for which the dual description consists of N f D7-branes in the background of N c black D3-branes, but our results apply in other dimensions as well. A non-zero chemical potential µ b or baryon number density n b is introduced via a nonvanishing worldvolume gauge field on the D7-branes. Ref.[1] identified a first order phase transition at zero density associated with 'melting' of the mesons. This extends to a line of phase transitions for small n b , which terminates at a critical point at finite n b . Investigation of the D7-branes' thermodynamics reveals that (∂µ b /∂n b ) T < 0 in a small region of the phase diagram, indicating an instability. We comment on a possible new phase which may appear in this region.

Three types of thick branes, i.e., Poincaré, de Sitter and Anti-de Sitter brane are considered. They are realized as the non-singular solutions of the Einstein equations with the non-trivial dilatons and the potentials. The scalar perturbations of these systems are also investigated. We find that the effective potentials of the master equations of the scalar perturbations are positive definite and consequently these systems are stable under the small perturbations.

The inflationary scenario for the brane world driven by the bulk inflaton is proposed. The quantum fluctuations of the inflaton is calculated and compared to those of the conventional 4-dimensional inflationary scenario. It is shown that the deviation of the primordial spectrum of this model from that of the conventional one is too small to be observed even if AdS radius is very large. Hence, it turns out that the inflation caused by the bulk inflaton is viable in the context of brane world cosmology.

We investigate cosmological evolutions of the bulk scalar field φ(t) and the radion d(t) in five-dimensional dilatonic two branes model. The bulk potential for the scalar field is taken as the exponential function V bulk ∝ exp(−2 √ 2bφ), where b is the parameter of the theory. This model includes Randall-Sundrum model (with b = 0) and fivedimensional Hořava-Witten theory (with b = 1). We consider matter on both branes and arbitrary potentials on the branes and in the bulk. These matter and potentials induce the cosmological expansion of the brane as well as the time evolution of the bulk scalar field and the radion. Starting with full five-dimensional equations, we derive four-dimensional effective equations which govern the low-energy dynamics of brane worlds. A correspondent five-dimensional geometry is also obtained. The effective fourdimensional theory on a positive tension brane is described by bi-scalar tensor theory.If the radion is stabilized, the effective theory becomes Brans-Dicke (BD) theory with BD parameter 1/2b 2 . On the other hand, if the scalar field is stabilized, the effective theory becomes scalar-tensor theory with BD parameter 3 2(3b 2 +1)where ϕ is the BD field defined by radion d(t). If we do not introduce the stabilization mechanism for these moduli fields, the acceptable late time cosmology can be realized only if the dilaton coupling b is small (b 2 < 1.6 × 10 −4 ) and the negative tension brane is sufficiently away from the positive tension brane. We also construct several models for inflationary brane worlds driven by potentials on the brane and in the bulk.

We study the tachyon condensation of the DD-brane system with a constant tachyon vev in the context of classical solutions of the Type II supergravity. We find that the general solution with the symmetry ISO(1, p) × SO(9 − p) (the three-parameter solution) includes the extremal black p-brane solution as an appropriate limit of the solution by fixing one of the three parameters (c 1 ). Furthermore, we compare the long distance behavior of the solution with the massless modes of the closed strings from the boundary state of the DD-brane system with a constant tachyon vev. We find that we must fix c 1 to zero and only two parameters are needed to express the tachyon condensation of the DD-brane system. This means that the parameter c 1 does not correspond to the tachyon vev of the DD-brane system.